Non-equilibrium Many-body Physics Beyond the Floquet Paradigm

While the physics of flat band systems, quasiperiodic disorder and many-body interactions have been important fields of activity, the in- terplay of these features has only scantily been explored. The poster will discuss the effect of many-body interactions and quasiperiodic Aubry André (????????) disorder on the one-dimensional all-band-flat (ABF) dia- mond lattice[1,2]. We show that coupling the ABF diamond lattice with nearest- neighbour interactions yields a non-ergodic phase independent of the strength of interaction. Interestingly, the resulting phases in the inter- acting diamond lattice depend on the symmetry and the strength of the applied quasiperiodic disorder. An exciting finding is the emergence of non-equilibrium quantum caging behaviour for specially engineered many-body initial states. Our work provides an insight into the phase diagram of an interacting flat band system subjected to quasiperiodic disorder via a non-equilibrium dynamical study. 1. Interplay of many-body interactions and quasiperiodic disorder in the all-band-flat diamond chain, PRB 107, 245110 (2023) 2.Flat-band-based multifractality in the all-band-flat diamond chain, PRB 106, 205119 (2022)

The interplay between interactions and disorder in many-body systems may suppress thermalization. Dynamical signatures of incipient many-body localization, in the form of very slow dynamics, are expected even in long-range interacting disordered many-body systems [1], but until recently have remained elusive. Such physics is realized in insulating salts that are doped with dipolar-interacting magnetic ions. In these systems, the slow many-body dynamics of typical dopants can be probed by emergent highly-coherent cluster degrees of freedom [2]. Indeed, pairs of close-by ions constitute ideal quantum sensors, as they can host long-lived, highly coherent excitations, which can be manipulated with optical pulses. Their ability to sense the dynamics in their environment is the result of a subtle second-order virtual exchange process. I will discuss how the coherence of such clusters can be significantly enhanced by exploiting cluster symmetry [3]. [1] Yao, N. Y., Laumann, C. R., Gopalakrishnan, S., Knap, M., Mueller, M., Demler, E. A., & Lukin, M. D. (2014). Many-body localization in dipolar systems. Physical Review Letters. [2] Beckert, A., Grimm, M., Wili, N., Tschaggelar, R., Jeschke, G., Matmon, G., Gerber, S., Müller, M., & Aeppli, G., (2024). Emergence of highly coherent two-level systems in a noisy and dense quantum network. Nature Physics. [3] Amato, L., Grimm, M. & Müller, M. (in preparation)

The emergence of classical chaos from an underlying quantum mechanics remains a challenging question due to the differences between dynamics driven by Schrodinger's equation versus Newton's equations. We present an infinite family of purely quantum recurrences that are not present in the classical limit of a chaotic system. They take the form of stroboscopic unitary evolutions in the quantum kicked top that act as the identity after a finite number of kicks. These state-independent recurrences are present in all finite dimensions and depend on the strength of the chaoticity parameter of the top. We further discuss the relationship of these periodicities to the quantum kicked rotor dynamics, and the phenomenon of quantum anti-resonance.

Light polarization and intensity serve as effective tools for modulating interactions with matter, enabling the induction of band hybridizations and topological phase transitions. This study explores the additional control achievable by manipulating the spatial phase dependence of light fields, particularly through vortex light beams carrying orbital angular momentum [1]. We investigate the impact of light-matter interaction on a two-dimensional massive Dirac-like system under the influence of a monochromatic vortex light beam [2]. Employing Floquet’s formalism, we define the total angular momentum in Floquet space precisely and identify the polarizations conducive to its conservation. Through the one-photon approximation, we correlate the resulting Hamiltonian with an s-wave superfluid model accommodating multiple quantized vortex core states [2]. This approach enables us to analytically predict the appearance of vortex states at low energies in our system. Expanding on these findings, we utilize the Bessel decomposition method to numerically diagonalize the complete Floquet Hamiltonian in the resonant regime. Consequently, we provide a comprehensive description of the photon-dressed electronic vortex states arising in the irradiated system, detailing their angular momentum-dependent dispersion relation and real-space extension. [1] Y. Shen, et al., Light: Science & Applications 8, 1–29 (2019) [2] L. I. Massaro, C. Meese, N. P. Sandler, and M. M. Asmar, arXiv:2404.09086 [cond-mat.mes-hall] (2024). [3] A. Prem, S. Moroz, V. Gurarie, and L. Radzihovsky, PRL 119, 067003 (2017)

Recently discovered measurement-induced transitions (MIPTs) in entanglement are phase transitions in classical simulability. However, some highly-entangling dynamics (e.g., integrable systems or Clifford circuits) are easy to classically simulate. Here, we study simulability transitions beyond entanglement by asking how the dynamics of magic competes with measurements. We find distinct MIPTs in magic, simulability, and entanglement. We identify dynamical "stabilizer-purification" as the mechanism driving the magic transition. En route, we use Pauli-based computation to distill the quantum essence of the dynamics to a set of measurements. We link stabilizer-purification to "magic fragmentation" wherein these measurements separate into disjoint, O(1)-weight blocks, and relate this to the spread of magic in the original circuit becoming arrested.

Levitons are single-electron excitations in metal (devoid of electron-hole pairs) which are usually created by applying a periodic voltage drive to a sample. The underlying mechanism behind these excitation therefore rely strongly on Floquet theory. After recalling the basics of Leviton physics in normal non-correlated junction, and through the example of an N-BCS junction, I will explore some Floquet features only present in correlated systems. The typical setup consists of a quantum point contact (QPC), separating two electrodes, and driven by a time-dependent potential difference. In the case where this drive is periodic, a Keldysh-Floquet approach can be developed, which allows to compute transport quantities such as the current and noise at the junction. Typically, the average current is understood within a Tien-Gordon picture, which has a straightforward interpretation in terms of the underlying Floquet formalism. When no correlations are present, the noise also fits in the Tien-Gordon picture, this allows to understand Levitons as Floquet states with only positive energy contributions. In this Poster, I will focus on BCS-like correlations in one of the leads, and show how, in general, this invalidates the Tien-Gordon picture of the noise. Then I will describe how Floquet theory helps us understand these complications, introducing correlation-driven interferences between different Floquet channels. Building on this understanding, a modified Tien-Gordon picture can be obtained in the infinite superconducting gap regime. In this case, the BCS correlation therefore create "composite Floquet channels" who support this modified Tien-Gordon picture.

By employing an open quantum systems framework, we investigate heat current within a quantum system interfaced with baths at distinct temperatures. While the Redfield equation is conventionally applied for such analyses, its applicability is restricted to weak coupling regimes. To address systems with stronger coupling to the environments, we adopt a non-perturbative approach utilizing the Hierarchical Equations of Motion [1]. This method enables exploration of regions characterized by strong coupling to the surrounding environments, offering a comprehensive understanding of heat dynamics. For this purpose, we have adapted the scalable DM-HEOM [2, 3] implementation to accommodate baths at different temperatures. \subsection{References} [1] Y. Tanimura, R. Kubo "Time evolution of a quantum system in contact with a nearly Gaussian-Markoffian noise bath" J. Phys. Soc. Jpn. 1989, 58, 101. [2] T. Kramer, M. Noack, A. Reinefeld, M. Rodríguez, and Y. Zelinskyy, “Efficient calculation of open quantum system dynamics and time-resolved spectroscopy with distributed memory HEOM (DM-HEOM),” doi: 10.1002/jcc.25354. [3] M. Noack, A. Reinefeld, T. Kramer and T. Steinke, "DM-HEOM: A Portable and Scalable Solver-Framework for the Hierarchical Equations of Motion," doi: 10.1109/IPDPSW.2018.00149.

Rydberg atoms provide a natural platform in order to study different Heisenberg spin models. As a dipolar spin glass phase has been controversial over decades, in this poster we present our Rydberg quantum simulation platform as a toolbox to study the interplay between disorder and magnetic frustration in an isolated dipolar spin system. We want to discuss ideas on the detection of a possible spin glass quantum phase transition, ageing and rejuvenation, as well as topics related to possible effects under periodic driving.

Intriguing dynamical quantum many-body effects such as prethermalisation, localisation, and emergence of topological states are usually studied theoretically under the assumption that the external drive, $\hat{V}(t)$, is time-periodic. This allows one to employ the Floquet theory and construct an effective time-independent Hamiltonian $\hat{H}_{{\rm eff}}$ that stroboscopically characterises dynamics of the system. However, effective Hamiltonians can be derived analytically in a few simple cases only. Otherwise, various high-frequency expansions prove useful, whereby $\hat{H}_{{\rm eff}}$ is constructed as an expansion in powers of $\hat{V}(t)/\omega$, where $\omega$ is the driving frequency. This procedure becomes particularly transparent when formulated in the Floquet--Hilbert space, wherein the time-dependent Hamiltonian is mapped onto a time-independent one (called the Floquet Hamiltonian or the quasienergy operator), represented by an infinite matrix possessing block structure. However, the high-frequency expansions currently described in the literature are inapplicable when the driving is resonant with transitions between states of the undriven system. In this work, we derive a high-frequency expansion that treats the case of resonant driving. The proposed extended degenerate perturbation theory thus alleviates the requirement that the driving frequency has to be much greater than the bandwidth of the spectrum of the unperturbed Hamiltonian. The derivation amounts to formulating a degenerate perturbation theory in the Floquet--Hilbert space and block-diagonalising the quasienergy operator to construct an approximation of $\hat{H}_{{\rm eff}}$. To demonstrate the validity of the derived expressions, we apply them to the driven Bose--Hubbard model and calculate the quasienergy spectrum (eigenvalues of $\hat{H}_{{\rm eff}}$), which are physically significant. We perform calculations for different resonant conditions $nU=m\omega$ ($U$ is the interaction strength of the Bose--Hubbard model; $n$ and $m$ are integers) and compare the results with numerically exact ones, which can only be obtained for small systems. The developed theory is seen to approximate the exact results in great detail.

We study a chaotic particle-conserving kinetically constrained model, with a single parameter which allows us to break reflection symmetry. Through extensive numerical simulations we find that the domain wall state shows a variety of dynamical behaviors from localization all the way to ballistic transport, depending on the value of the reflection breaking parameter. Surprisingly, such anomalous behavior is not mirrored in infinite-temperature dynamics, which appear to scale diffusively, in line with expectations for generic interacting models. However, studying the particle density gradient, we show that the lack of reflection symmetry affects infinite-temperature dynamics, resulting in an asymmetric dynamical structure factor. This is in disagreement with normal diffusion and suggests that the model may also exhibit anomalous dynamics at infinite temperature in the thermodynamic limit. Finally, we observe low-entangled eigenstates in the spectrum of the model, a telltale sign of quantum many body scars.

Commonly, the notion of “quantum chaos” refers to the fast scrambling of information throughout complex quantum systems undergoing unitary evolution. Motivated by the Krylov complexity and the operator growth hypothesis, we demonstrate that the entropy of the population distribution for an operator in time is a useful way to capture the complexity of the internal information dynamics of a system when subject to an environment and is, in principle, agnostic to the specific choice of operator basis. We demonstrate its effectiveness for the Sachdev-Ye-Kitaev (SYK) model, examining the dynamics of the system in both its Krylov basis and the basis of operator strings. We prove that the former basis minimises spread complexity while the latter is an eigenbasis for high dissipation. In both cases, we probe the long-time dynamics of the model and the phenomenological effects of decoherence on the complexity of the dynamics.

We analyse how the simple local constraints encoded by the ice model in two dimensions lead a defect to exhibit robust, and tunable, subdiffusive behaviour, while the growth of the frontier of its cluster is described by SLE(2), at variance with growth models in the KPZ or SLE(8/3) universality class. We provide complementary perspectives providing intuitive, and quantitative, insights linking microscopics, numerical simulations and effective theories (loop erased random walks, fractional diffusion, height models). We discuss potential realizations of this physics in cold atomic simulation platforms, as well as artificial and chemical structures.

Studying the influence of a weakly perturbed flat band on transport of interacting particles reveals anomalous diffusion and prethermalization. For very weak perturbations transport is getting slower than regular diffusion because of repulsive particle-particle interaction. The effect can be understood by a canonical transformation of dispersive and flat band eigenstates into a basis of light and heavy quasiparticles which are trapping each other. They are subjected to orbital conservation laws what enables a treatment of the phenomenon in terms of the Born-Oppenheimer approximation and allows an illustration in a familiar physical picture analogous to electrons and nuclei. This approach furthermore sheds light on the thermalization process in such a system in general. Methodology: Transport properties are calculated by simulating the broadening of initially localized wave packets of spinless fermions in a quasi one-dimensional Hubbard model with three-orbital diamond structure. Initial states are constructed in the framework of dynamical quantum typicality. Time evolution is performed by either the Lanczos algorithm or full diagonalization if possible.

In the quantum system under periodical modulation, the particle can be excited by absorbing the laser photon with the assistance of integer Floquet photons, so that the Floquet sidebands appear. Here, we experimentally observe non-integer Floquet sidebands (NIFBs) emerging between the integer ones while increasing the strength of the probe laser in the optical lattice clock system. Then, we propose the Floquet channel interference hypothesis (FCIH) which surprisingly matches quantitatively well with both experimental and numerical results. With its help, we found both Rabi and Ramsey spectra are very sensitive to the initial phase and exhibit additional two symmetries. More importantly, the height of Ramsey NIFBs is comparable to the integer one at larger $g/\omega$ s which indicates an exotic phenomenon beyond the perturbative description.

An intriguing regime of universal charge transport at high entropy density has been proposed for periodically driven interacting one-dimensional systems with Bloch bands separated by a large single-particle band gap. For weak interactions, a simple picture based on well-defined Floquet quasiparticles suggests that the system should host a quasisteady state current that depends only on the populations of the system's Floquet-Bloch bands and their associated quasienergy winding numbers. Here we show that such topological transport persists into the strongly interacting regime where the single-particle lifetime becomes shorter than the drive period. Analytically, we show that the value of the current is insensitive to interaction-induced band renormalizations and lifetime broadening when certain conditions are met by the system's non-equilibrium distribution function. We show that these conditions correspond to a quasisteady state. We support these predictions through numerical simulation of a system of strongly interacting fermions in a periodically-modulated chain of Sachdev-Ye-Kitaev dots. Our work establishes universal transport at high entropy density as a robust far from equilibrium topological phenomenon, which can be readily realized with cold atoms in optical lattices.

Current developments in topological quantum computing need experimental study of excitations with unusual statistics such as anyons. However, in order to get systems in this form we first need to excite an initial ground state. In this poster, I present the Kibble-Zurek mechanism which gives the scaling of excitations when we ramp through a phase transition. I apply this to the Kitaev Honeycomb Model which is a good toy model to study anyons. I get different scaling of excitations depending on the phase transition, I get in particular for one phase transition some logarithmic correction to the usual scaling given by the Kibble-Zurek mechanism.

The study of chaos and integrability in open quantum many-body systems is central in many research areas ranging from high-energy physics to condensed matter, quantum optics, and quantum technologies. We introduce the notions of steady-state and transient quantum chaos along the dynamics of open quantum systems, showing how they explain several phenomena that would otherwise remain elusive. We provide a new criterion for the characterization of dissipative quantum chaos, which outperforms other current methods. We study the emergence of steady-state and transient quantum chaos in the driven-dissipative Bose-Hubbard model, demonstrating that our theoretical framework enables a comprehensive understanding of system's phase diagram. We finally illustrate how our theory qualitatively and quantitatively explains the experimental results, in particular the development of dissipative quantum chaos in an experimentally realized open Floquet system.

We establish a method based on Floquet theory to efficiently determine and examine instabilities of microscopic magnon systems such as thin films of ferro- or ferri-magnetic materials. A special feature of parametric resonance is the possibility to excite magnons with higher energy than the driving frequency, which allows for new tuning possibilities. We examine regions of resonances for frequencies below the energy spectrum and predict different effects depending on the driving amplitude and frequency, like the vanishing of instabilities at high driving fields. Further we derive analytic prediction for resonance thresholds and regions of resonance. We compare our results with phenomenological approaches to investigate the role damping plays in such systems and perform micromagnetic simulations in order to confirm our results.

We show that the matrix product state (MPS) provides a thermal quantum pure state (TPQ) representation in equilibrium in two spatial dimensions over the entire temperature range. We use the Kitaev honeycomb model as a prominent, non-trivial example hosting a quantum spin liquid (QSL) ground state. Our method is able to qualitatively capture the double-peak in the specific heat, which was previously obtained nearly exactly using a method tailored to the Kitaev honeycomb model. In contrast, our method can be applied to general systems including those with competing interactions. We also demonstrate, that the truncation process efficiently discards the high-energy states, eventually reaching the long-range entangled topological state with very low statistical errors.

The Jordan-Wigner map in two dimensions is an exact lattice regularization of the $2 \pi$-flux attachment to a hard-core boson (or spin $\frac{1}{2}$) leading to a composite fermion particle. When the spin-$\frac{1}{2}$ model obeys ice rules this map preserves locality, namely, local Rohkshar-Kivelson (RK) models of spins are mapped onto local models of Jordan-Wigner composite fermions. Using this composite fermion dual representation of RK models we construct spin-liquid states by projecting Slater determinants onto the subspaces of the ice rules. Interestingly, we find that these composite fermions behave as “dipolar” partons for which the projective implementations of symmetries are very different from standard “pointlike” partons. We construct interesting examples of these composite Fermi-liquid states that respect all microscopic symmetries of the RK model. In the six-vertex subspace, we constructed a time-reversal and particle-hole-invariant state featuring two massless Dirac nodes, which is a composite fermion counterpart to the classic $\pi$-flux state of Abrikosov fermions in the square lattice. This state is a good ground-state candidate for a modified RK–type Hamiltonian of quantum spin ice. In the dimer subspace, we constructed a state featuring a composite Fermi surface but with nesting instabilities towards ordered phases such as the columnar state. We have also analyzed the low-energy emergent gauge structure. If one ignores confinement, the system would feature a $U(1)\times U(1)$ low-energy gauge structure with two associated gapless photon modes, but with the composite fermion carrying gauge charge only for one photon and behaving as a gauge-neutral dipole under the other. These states are also examples of pseudoscalar $U(1)$ spin liquids where mirror and time-reversal symmetries act as composite fermion particle-hole conjugations, and the emergent magnetic fields are even under such time-reversal or lattice mirror symmetries.

Tilted lattice potentials with periodic driving play a crucial role in the study of artificial gauge fields and topological phases with ultracold quantum gases. However, driving-induced heating and the growth of phonon modes restrict their use for probing interacting many-body states. By experimentally investigating phonon modes and interaction-driven instabilities of superfluids in the lowest band of a shaken optical lattice, we identified stable and unstable parameter regions and provided a general resonance condition. In contrast to the high-frequency approximation of a Floquet description, we directly used the superfluids' micromotion to analyze the growth of phonon modes from slow to fast driving frequencies. Our observations enable the prediction of stable parameter regimes for quantum-simulation experiments aimed at studying driven systems with strong interactions over extended time scales.

We uncover emergent universality arising in the equilibration dynamics of multimode continuous-variable systems. Specifically, we study the ensemble of pure states supported on a small subsystem of a few modes, generated by Gaussian measurements on the remaining modes of a globally pure bosonic Gaussian state. We find that beginning from sufficiently complex global states, such as random Gaussian states and product squeezed states coupled via a deep array of linear optical elements, the induced ensemble attains a universal form, independent of the choice of measurement basis: it is composed of unsqueezed coherent states whose displacements are distributed normally and isotropically, with variance depending on only the mean particle number of the system. We further show that the emergence of such a universal ensemble is consistent with a generalized maximum-entropy principle, and has a unique quantum information-theoretic property of having minimal accessible information. Our results represent a conceptual generalization of the recently introduced notion of "deep thermalization" in discrete-variable quantum many-body systems -- a novel form of equilibration going beyond thermalization of local observables -- to the realm of continuous-variable quantum systems. Moreover, it demonstrates how quantum information-theoretic perspectives can unveil new physical phenomena and principles in quantum dynamics and statistical mechanics.

We study equilibrium and dynamical phase diagrams of an interacting system of N-component charged bosons with dipole symmetry. In the large N limit, the equilibrium phase diagram of these bosons shows a first-order transition between two phases. The first one is a localized normal phase where both the global U(N) and the dipole symmetries are conserved and the second one is a delocalized condensed phase where both the symmetries are broken. In contrast, the steady state after an instantaneous quantum quench from the condensed phase shows an additional, delocalized normal phase, where the global U(N) symmetry is conserved but the dipole symmetry is broken, for a range of the quench parameters. A study of the ramp dynamics of the model shows that the above-mentioned steady state exists only above a critical ramp rate.

We find that the presence of strong non-Abelian conserved quantities can lead to highly entangled stationary states even for unital quantum channels. We derive exact expressions for the bipartite logarithmic negativity, Rényi negativities, and operator space entanglement for stationary states restricted to the trivial symmetry subspace. We find a general upper bound for all these quantities given by the logarithm of the dimension of the commutant algebras(which characterize the strongly-conserved quantities). This indicates that the logarithmic negativity scales at most O($1$) for non-Abelian finite groups, at most logarithmically for SU($N$) groups, and can be a volume-law for fragmentation.

Understanding quantum many-body systems far-from-equilibrium is an important but challenging problem, finding relevance in condensed matter, high-energy, and quantum information. Solvable models of quantum dynamics are therefore desirable, but rare. Here we introduce a family of quantum circuits whose entanglement dynamics is exactly solvable, leveraging new ideas of dualities between space-time known as generalized dual-unitarity. We find rich phenomenology ranging from universal quantum chaotic behavior, to conceptually novel non-chaotic yet non-integrable dynamics. Our work extends our knowledge of different classes of interacting quantum dynamics, and provides analytical testbeds to probe interesting physical phenomena like quantum thermalization and information scrambling.

Dual-unitary circuits are a class of quantum systems for which exact calculations of various quantities are possible, even for circuits that are nonintegrable. The array of known exact results paints a compelling picture of dual-unitary circuits as rapidly thermalizing systems. However, in this Letter, we present a method to construct dual-unitary circuits for which some simple initial states fail to thermalize, despite the circuits being “maximally chaotic,” ergodic, and mixing. This is achieved by embedding quantum many-body scars in a circuit of arbitrary size and local Hilbert space dimension. We support our analytic results with numerical simulations showing the stark contrast in the rate of entanglement growth from an initial scar state compared to nonscar initial states. Our results are well suited to an experimental test, due to the compatibility of the circuit layout with the native structure of current digital quantum simulators.

Symmetry Topological Field Theory (SymTFT) is a framework to capture universal features of quantum many-body systems by viewing them as a boundary of topological order in one higher dimension. This has yielded numerous insights in static low-energy settings. Here we study what SymTFT can reveal about nonequilibrium, focusing on one-dimensional (1D) driven systems and their 2D SymTFTs. In driven settings, boundary conditions (BCs) can be dynamical and can apply both spatially and temporally. We show how this enters SymTFT via topological operators, which we then use to uncover several new results. These include revealing time crystals (TCs) as systems with symmetry-twisted temporal BCs, finding robust bulk “dual TCs” in phases thought to be only boundary TCs, generating drive dualities, or identifying 2D Floquet codes as space-time duals to 1D systems with duality-twisted spatial BCs. We also show how, by making duality-twisted BCs dynamical, non-Abelian braiding of duality defects can enter SymTFT, leading to effects such as the exact pumping of symmetry charges between a system and its BCs. We illustrate our ideas for Z2-symmetric 1D systems, but our construction applies for any finite Abelian symmetry.

We present the analysis of the slowing down exhibited by stochastic dynamics of a ring-exchange model on a square lattice, by means of numerical simulations. We find the preservation of coarse-grained memory of initial state of density-wave types for unexpectedly long times. This behavior is inconsistent with the prediction from a low frequency continuum theory developed by assuming a mean-field solution. Through a detailed analysis of correlation functions of the dynamically active regions, we exhibit an unconventional transient long ranged structure formation in a direction which is featureless for the initial condition, and argue that its slow melting plays a crucial role in the slowing-down mechanism. We expect our results to be relevant also for the dynamics of quantum ring-exchange dynamics of hard-core bosons and more generally for dipole moment conserving models.

Entanglement membrane theory is an effective coarse-grained description of entanglement dynamics and operator growth in chaotic quantum many-body systems. The fundamental quantity characterizing the membrane is the entanglement line tension. However, determining the entanglement line tension for microscopic models is in general exponentially difficult. We compute the entanglement line tension in a recently introduced class of exactly solvable yet chaotic unitary circuits, so-called generalized dual-unitary circuits, obtaining a non-trivial form that gives rise to a hierarchy of velocity scales with $v_E

We provide numerical evidence, based on infinite matrix product state methods, for the universality of the quasi-Fermi liquid in a class of interacting fermion lattice Hamiltonians. This paradigm combines features of both Luttinger and Fermi liquids. Our study explores its universal structure based on the spectral function and dynamic structure factor. Quasi-particles may be present in either particle or hole sectors for half-filled systems, while power-law excitations occur away from half-filling. The dynamic structure factor exhibits free-fermion-like behavior at low energies and high-energy well-defined excitation branches. These results establish the quasi-Fermi liquid as a unique phase of quantum fermions in one spatial dimension.

We propose a time-crystal model based on a disordered interacting long-range spin chain where the periodic swapping of nearby spin couples is applied. This protocol can be applied to systems with any local spin magnitude s and in principle also to systems with nonspin (fermionic or bosonic) local Hilbert space. We explicitly consider the cases s=1/2 and s=1, using analytical and numerical methods to show that the time-crystal behavior appears in a range of parameters. In particular, we study the persistence of period-doubling oscillations in time, the properties of the Floquet spectrum (π-spectral pairing and correlations of the Floquet states), and introduce a quantity (the local imbalance) to assess what initial states give rise to a period-doubling dynamics. We also use a probe of quantum integrability/ergodicity to understand the interval of parameters where the system does not thermalize, and a nontrivial persistent period-doubling behavior is possible.

Over the last decade, periodic (Floquet) drives have emerged as a useful technique to engineer the properties of quantum systems. Additionally, periodically driven systems can manifest nonequilibrium phases of matter without static counterparts, such as discrete time crystals or anomalous topological insulators. The ability to realize effective Hamiltonians with properties drastically different from those of the non-driven system, makes Floquet engineering a vital ingredient in present-day quantum simulators. However, the manipulation of the states dressed by strong periodic drives remains an outstanding challenge in Floquet engineering. The state-of-the-art in Floquet control is the adiabatic change of parameters. Yet, this requires long protocols conflicting with the limited coherence times in experiments. This poster presents Floquet Counterdiabatic Driving, a generalization of variational counterdiabatic driving to Floquet systems, that enables transitionless driving of Floquet eigenstates far away from the adiabatic regime. In particular, we present a nonperturbative variational principle to find local approximations to the Floquet adiabatic gauge potential. The Floquet adiabatic gauge potential is also closely related to the response functions of the Floquet system.

Motivated by an experiment on a superconducting quantum processor [Mi et al., Science 378, 785 (2022)], we study level pairings in the many-body spectrum of the random-field Floquet quantum Ising model. The pairings derive from Majorana zero and $\π$ modes when writing the spin model in Jordan-Wigner fermions. Both splittings have lognormal distributions with random transverse fields. In contrast, random longitudinal fields affect the zero and $\π$ splittings in drastically different ways. While zero pairings are rapidly lifted, the $\π$ pairings are remarkably robust, or even strengthened, up to vastly larger disorder strengths. We explain our results within a self-consistent Floquet perturbation theory and study implications for boundary spin correlations. The robustness of $\π$ pairings against longitudinal disorder may be useful for quantum information processing.

We demonstrate: 1) the existence of a non-equilibrium "Floquet Fermi Liquid" state in partially filled Floquet Bloch bands, weakly connected to ideal fermionic baths. This state features a series of nested "Floquet Fermi surfaces" akin to matryoshka dolls. We explore its properties, such as quantum oscillations under magnetic fields, revealing slow amplitude beatings related to the Floquet Fermi surfaces' different areas, aligning with observations in microwave-induced resistance oscillation experiments. Additionally, we demonstrate the tunability of some Floquet Fermi surfaces towards non-equilibrium van-Hove singularities by altering the drive's frequency, without affecting electron density. 2) the existence of a quantum non-equilibrium steady state in periodically driven fermions coupled to a bosonic bath, distinct from any equilibrium counterpart. This state displays multiple distinct Fermi surfaces marked by higher order cusp-like non-analyticities in momentum occupation, lacking an associated jump or quasiparticle residue, thus categorizing these as non-equilibrium non-Fermi liquids. Remarkably, these non-analyticities persist even at finite bath temperatures, a unique feature not seen in equilibrium Fermi or non-Fermi liquids, where temperature typically blurs such sharp features.

A non-equilibrium state shares macroscopic properties, such as conductivity and superconductivity, with a static state when the two states exhibit an identical average value of an observable over a period. We studied the quench dynamics of a Kitaev chain on the basis of two types of order parameters associated with two channels of pairing: local pairing in real space and Bardeen-Cooper-Schrieffer (BCS)-like pairing in momentum space. Based on the exact solution, we found that the two order parameters were identical for the ground state, which indicated a balance between the two pairing channels and would help determine the quantum phase diagram. However, for a nonequilibrium state obtained through time evolution from an initially prepared vacuum state, the two parameters varied, but both parameters could still help determine the phase diagram. In the region of nontrivial topological phases, nonequilibrium states favored BCS-like pairing. In this paper, we present an alternative approach to dynamically generate a superconducting state from a trivial empty state and illuminate the pairing mechanism.

Hilbert space fragmentation is an intriguing paradigm of ergodicity breaking in interacting quantum manybody systems with applications to quantum information technology, but it is usually adversely compromised in the presence of perturbations. In this work, we demonstrate the protection of constrained dynamics arising due to a combination of mirror symmetry and Hilbert space fragmentation by employing the concept of quantum Zeno dynamics. We focus on an Ising spin ladder with carefully chosen quantum fluctuations, which in the ideal case guarantee a perfect disentanglement under Hamiltonian dynamics for a large class of initial conditions. This is known to be a consequence of the interplay of Hilbert space fragmentation with a mirror symmetry, and we show numerically the effect of breaking the latter. To evince the power of this perfect disentanglement, we study the effect of generic perturbations around the fine-tuned model and show that we can protect against the undesirable growth of entanglement entropy by using a local Ising interaction on the rungs of the ladder. This allows us to suppress the entanglement entropy to an arbitrarily small value for an arbitrarily long time by controlling the strength of the rung interaction. Our work demonstrates the experimentally feasible viability of quantum Zeno dynamics in the protection of quantum information against thermalization.

Exploring continuous time crystals (CTCs) within the symmetric subspace of spin systems has been a subject of intensive research in recent times. Thus far, the stability of the time-crystal phase outside the symmetric subspace in such spin systems has gone largely unexplored. Here, we investigate the effect of including the asymmetric subspaces on the dynamics of CTCs in a driven dissipative spin model. This results in multistability, and the dynamics becomes dependent on the initial state. Remarkably, this multistability leads to exotic synchronization regimes such as chimera states and cluster synchronization in an ensemble of coupled identical CTCs.

Abstract: Quantization of particle transport lies at the heart of topological physics. In Thouless pumps -- dimensionally reduced versions of the integer quantum Hall effect -- quantization is dictated by the integer winding of single-band Wannier states. Here, we show that repulsive interactions can stabilize a prethermal fractional Thouless pump resulting from the fractional winding of multiband Wannier states. To this end, we consider an Aubry-André chain with five sites and one fermion per unit cell which has a pair of low lying Thouless-pumping bands. If the repulsion is sufficiently strong the favored state is a Wigner crystal that spontaneously populates one subspecies of multi-band Wannier states of the low energy bands. As these return to themselves only after two periods of the drive the state can be viewed as a time crystal, and exhibits fractional charge pumping. However, due to the single-particle energy difference between different species of multiband Wannier states, the pump cycle forces the Wigner crystal over a background of large domain excitations, the production rate of which sets the prethermal lifetime of the fractional pump. By analogy to the problem of false vacuum decay we argue that the production rate of such excitations is exponentially suppressed in the ratio of interaction strength to the combined bandwidth of the low energy bands. To arrive at these conclusions we employ exact diagonalization studies of short chains, giving a phase diagram in terms of pumped charge and quantization lifetime as a function of interaction strength and pump frequency. We extend our results to long chains through a mean field analysis augmented by an effective model for the domain excitations. Our model may be directly realized in cold atom experiments.

Recent research works on periodically and aperiodically driven systems have revealed a number of novel, interesting non-equilibrium phenomena. Electric field-driven systems are a particularly important subclass from the perspective of Floquet engineering. We study the non- trivial dynamics of the delocalized and localized phases of a family of time-periodic and aperi- odic electric-field driven quantum systems in the non-interacting and interacting limits. We find that in the presence of disorder low-frequency periodic driving leads to subdiffusive transport in both the non-interacting and interacting limits. Next, the study of aperiodically (Fibonacci and Thue-Morse) driven systems again shows anomalous transport in both the non-interacting and interacting limits. We also observe a dependence of the mean squared displacement with the driving frequency. We also study periodically and quasi-periodically driven long-range interacting systems and investigate the dynamics leading to thermalization. The interplay of periodic driving and long-range interaction results in frozen dynamics of the system, and hence suppression of heat- ing for a longer time if we tune the driving at a high frequency. Interestingly, in the presence of quasiperiodic driving (Fibonacci, and Thue-Morse), we again find that the dynamics get slower with an increase in the range of interaction.

Quantum interacting many-body systems attract currently remarkable interest. I will exemplify these studies considering kicked spin chains. A method especially convenient to describe the short-time behavior of these systems in the limit of many constituents is the dual operator. In contrast to the Floquet operator that evolves the system in time, the dual operator evolves the system in particle direction. I will show numerically and analytically how localization and universal (chaotic) system properties manifest within the dual-operator approach.

We explore how interactions can facilitate classical-like dynamics in quantum Floquet models with sequentially activated hopping. Specifically, we add local and short range interaction terms to classes of Floquet Hamiltonians and ask for conditions ensuring the evolution acts as a permutation on initial local number Fock states. We show that at certain values of hopping and interactions, determined by a set of Diophantine equations, such evolution can be realized. When only a subset of the Diophantine equations is satisfied the Hilbert space can be fragmented into frozen states, states obeying cellular automata like evolution, and subspaces where evolution mixes Fock states and is associated with eigenstates exhibiting high entanglement entropy and level repulsion. When disorder is added to these systems, the dynamics may be stabilized in regions of parameter space away from these special parameter values - via k-body (or many-body) localization - to create new families of interesting phases. These families of phases also include phases already of current interest such as (correlation-induced) anomalous Floquet topological insulators.

The problem of a Kondo impurity coupled to a non-interacting bath is a cornerstone in understanding strongly correlated electron systems like heavy-fermion materials and quantum dots. However, it is largely unexplored what will happen when the bath is also strongly interacting. In this work, we theoretically study the ground-state properties and out-of-equilibrium dynamics when a Kondo impurity coupled to 1D and 2D attractive Hubbard bath, which is a paradigmatic setup to explore the interplay between the strong interactions both in the impurity and the bath, and capturing the central behavior of a magnetic impurity coupled to a superconductor. First, we find the ground state exhibits a singlet-doublet phase transition, and observe the competition between the Kondo correlation and the superconducting (SC) order. In particular, the SC order parameter on the two sides of the 1D chain exhibits an intriguing $\pi$ phase shift upon the formation of the Kondo singlet. Then we study the relaxation dynamics of the impurity coupled to a 2D bath, and observe a fast buildup of Kondo correlation near the impurity, associated with the emission of an amplitude-decaying spin-wave. Finally, we explore the transport dynamics between two 1D chains connected by the Kondo impurity and discover a myriad of dynamic behaviors, including the Josephson effect with small Kondo coupling, dynamic competition among charge, magnetic, and SC orders with intermediate coupling, and ballistic charge transport with large coupling associated with a dynamical breaking of the Kondo singlet under a high bias voltage. Our findings indicate rich avenues for exploration when an interacting quantum impurity couples with an interacting bath, and potentially lay a theoretical foundation for quantum simulations of superconductor-quantum dot devices. ref: Z.Y.Wei, E.Demler, J. I.Cirac, T.Shi, in preparation.

A system under periodic driving can be described by Floquet theorem, wherein the micromotion operator exhibits the same periodicity as the drive. However, when the driving becomes quasiperiodic, we find that the system could response chaotically, even in a single qubit. In this work, we demonstrate the obstruction to the existence of the quasienergy state and investigate chaotic responses in single-qubit driven systems. Additionally, we analyze the dynamic phase transition between quasiperiodic and chaotic time evolution.

We study temporal entanglement in dual-unitary Clifford circuits with probabilistic measurements preserving spatial unitarity. We exactly characterize the temporal entanglement barrier in the measurement-free regime, exhibiting ballistic growth and decay and a volume-law peak. In the presence of measurements, we show that the initial ballistic growth of temporal entanglement with bath size is modified to diffusive, which can be understood through a mapping to a persistent random walk model. The peak value of the temporal entanglement barrier exhibits volume-law scaling for all measurement rates. Additionally, measurements modify the ballistic decay to the "perfect dephaser limit" with vanishing temporal entanglement to an exponential decay, which we describe through a spatial transfer matrix method. The spatial dynamics is shown to be described by a non-Hermitian hopping model, exhibiting a PT-breaking transition at a critical measurement rate p=1/2.

Quantum dynamics with local interactions in lattice models display rich physics, but is notoriously hard to study. Dual-unitary circuits allow for exact answers to interesting physical questions in clean or disordered one- and higher-dimensional quantum systems. However, this family of models shows some non-universal features, like vanishing correlations inside the light-cone and instantaneous thermalization of local observables. In this work we propose a generalization of dual-unitary circuits where the exactly calculable spatial-temporal correlation functions display richer behavior, and have non-trivial thermalization of local observables. This is achieved by generalizing the single-gate condition to a hierarchy of multi-gate conditions, where the first level recovers dual-unitary models, and the second level exhibits these new interesting features. We also extend the discussion and provide exact solutions to correlators with few-site observables and discuss higher-orders, including the ones after a quantum quench. In addition, we provide exhaustive parametrizations for qubit cases, and propose a new family of models for local dimensions larger than two, which also provides a new family of dual-unitary models.

The Rydberg blockade mechanism is an important ingredient in quantum simulators based on neutral atom arrays. It enables the emergence of a rich variety of quantum phases of matter, such as topological spin liquids. The typically isotropic nature of the blockade effect, however, restricts the range of natively accessible models and quantum states. In this work, we propose a method to systematically overcome this limitation, by developing gadgets, i.e., specific arrangements of atoms, that transform the underlying Rydberg blockade into more general constraints. We apply this technique to realize dimer models on square and triangular geometries. In these setups, we study the role of the quantum fluctuations induced by a coherent drive of the atoms and find signatures of $U(1)$ and $\mathbb{Z}_2$ quantum spin liquid states in the respective ground states. Finally, we show that these states can be dynamically prepared with high fidelity, paving the way for the quantum simulation of a broader class of constrained models and topological matter in experiments with Rydberg atom arrays.

Superconducting systems driven by periodic light has been studied for a long time. One progress is the recent observation of microwave-driven Andreev steady state in the Josephson junction [1]. Here, we studied the Floquet steady states under periodical light driving for a BCS superconductor coupled to a heat bath [2]. We apply the Keldysh formalism in the Floquet representation [3] and derive a set of self-consistent equations for the superconducting order parameter. Our computing formalism is capable of dealing with large driving amplitude and high order of Floquet sidebands. The phase diagram in the space of frequency and amplitude of the light is computed. In the high-frequency regime, we find the superconducting order is enhanced following the effect of dynamical localization. In the low-frequency regime, another type of enhancement can be observed, which is accompanied by a characteristic non-thermal distribution of quasiparticles and is similar to the Eliashberg effect [4]. The evolution of superconductivity between two regimes is also computed uniformly by our formalism. [1] S. Park, W. Lee, S. Jang et al., Nature 603, 421–426 (2022). [2] H. Zhang, K. Taksan, N. Tsuji, in preparation. [3] N. Tsuji, T. Oka, and H. Aoki, Phys. Rev. B 78, 235124 (2008). [4] G. M. Eliashberg, JETP Lett. 11, 114 (1970).