Korrelationstage 2021

The Planckian time tau ~ hbar/(k T) is ubiquitous in both conventional and unconventional condensed matter systems. It has been proposed that the Planckian time may correspond to an absolute bound on quantum dynamics. I will discuss somewhat down-to-earth aspects of Planckian scattering in conventional metals and unconventional metals. I will end with some ideas about the role of electrons and phonons in high Tc materials.

We demonstrate a remarkable property of metallic Fermi liquids: the transverse conductivity assumes a universal value in the quasi-static ($\omega\to 0$) limit for wavevectors $q$ in the regime $l\ll q\ll p_F$, where $l$ is the mean free path and $p_F$ is the Fermi momentum. This value is $(e^2/h)*\rho/q$ in two dimensions, where $\rho$ measures the local radius of curvature of the Fermi surface in momentum space. Even more surprisingly, we find that U(1) spin liquids with a spinon Fermi surface have the same universal transverse conductivity. This means such spin liquids behave effectively as metals in this regime, even though they appear insulating in standard transport experiments. Moreover, we show that transverse current fluctuations result in a universal low-frequency magnetic noise that can be directly probed by a spin qubit, such as a nitrogen-vacancy center in diamond, placed at a distance $z$ outside of the metal or spin liquid. Specifically the magnetic noise is given by $C*omega*P/z$, where $P$ is the perimeter of the Fermi surface in momentum space and $C$ is a combination of fundamental constants of nature. Therefore these observables are controlled purely by the geometry of the Fermi surface and are independent of kinematic details of the quasiparticles, such as their effective mass and interactions. This behavior can be used as a new technique to measure the size of the Fermi surface of metals and as a smoking gun probe to pinpoint the presence of the elusive spinon Fermi surface in two-dimensional systems. We estimate that this universal regime is within reach of current nitrogen-vacancy center spectroscopic techniques for several spinon Fermi surface candidate materials.

Lifshitz transitions, in which the topology of a Fermi surface changes as a function of some tuning parameter, are of fundamental interest as examples of phase transitions that are associated with a change in topology but not a broken symmetry. Measurements of the stress-strain relation offer a thermodynamic probe of changes in the electronic free energy associated with changes in the Fermi surface. We studied Sr$_2$RuO$_4$, a correlated electron system that can be tuned through a Lifshitz transition with uniaxial pressure. Using a piezo-based apparatus, we investigated stress-driven changes in the electronic structure of Sr$_2$RuO$_4$ by measuring its Young's modulus as a function of pressure and temperature. We find that the Young's modulus exhibits a pronounced softening as the material passes through the Lifshitz transition, followed by hardening at higher stress. We aim to see if correlations have a substantial effect on the behaviour that we observe.

Understanding the behavior of an impurity strongly interacting with a Fermi sea is a long-standing challenge in many-body physics. When the interactions are short ranged, two vastly different ground states exist: a polaron quasiparticle and a molecule dressed by the majority atoms. In the single-impurity limit, it is predicted that at a critical interaction strength, a first-order transition occurs between these two states. Experiments, however, are always conducted in the finite temperature and impurity density regime. The fate of the polaron-to-molecule transition under these conditions, where the statistics of quantum impurities and thermal effects become relevant, is still unknown. In my talk, I will address this question theoretically and experimentally.

The experimental observation of the persistence of spin excitations in the doped cuprates is one of the main unresolved issues in the "high-$T_c$ problem" [1]. It is broadly believed that these excitations have a collective nature and they are hence usually referred to as paramagnons. On the other hand, the long-range magnetic order disappears at a very low hole-doping level. To resolve this paradox, we revisit this widely-studied problem and calculate the spin structure factor of a doped t-J model using state of the art DMRG on a 6x6 square lattice. The main result is that the properties of the magnetic spectra can be understood as originating only from very short-range magnetic correlations. [1] M. Le Tacon et al., Nature Physics 7, 725 (2011) ; M. P. M. Dean et al., Nature Materials 12, 1019 (2013).

In the recent decade, driving matters with ultrastrong electromagnetic fields has emerged as a promising pathway to manipulate properties of quantum materials on the ultrafast timescale. The interplay between light and electronic states has been shown to induce intriguing phenomena, including dynamical phase transition, e.g., resistive switching, and nonthermal states of matter. In these scenarios, the laser has often been modelled as a classical field, which can be reasonable, provided the laser pulse is strong and contains a macroscopic number of photons, i.e., a semiclassical coherent state. Recently, a different pathway for light-induced phases nevertheless emerges due to the implementation of ultrastrong light-matter coupling (USC) in cavity quantum electrodynamics (QED). This technological advance gives rise to the tantalizing possibility of significantly enhancing quantum fluctuations of the light confined in a small cavity and creating entangled light-matter phases for quantum materials coupled to the cavity modes. The USC regime, in which the material strongly couples to few-photon states or even the electromagnetic vacuum, represents a fundamentally different situation from the classical laser-driving, and leads to a quantum extension of the classical light-induced hidden phases: the QED engineering of materials. In this talk, I will explore the novel phases induced by quantum lights in both equilibrium and nonequilibrium, with an emphasis on the intertwining of strong electronic correlation and photon excitations. I will first discuss the systematic way to derive Hamiltonians describing solids strongly coupled to cavity photons and demonstrate that a nonlinear light-matter coupling term is inevitable to preserve the gauge-invariance. We further show the strong light-matter coupling can lead to a significant modification of the electron band structure and can be entangled with the competing orders in correlated materials, leading to the on-demand enhancement of different thermal and nonthermal orders. We also show that flat band structure and one-dimensional physics can emerge under certain cavity geometries. Moreover, long-range interactions of different natures can emerge due to the nonlinear coupling, giving rise to different types of superconducting orders. The conclusions are discussed with combined analytic and numerical methods, including the Power-Zienau-Woolley transformation, adiabatic elimination, and numerical exact diagonalization. Our results establish a systematic formalism of exploring the possibility of engineering various solid-state phenomena, particularly strong correlation physics, using quantum lights.

Recently, the possibility of inducing superconductivity for electrons in two dimensional materials has been proposed via cavity-mediated pairing. In this talk, I will discuss why photons are more interesting as a mediator of the pairing with respect to the phonons of the standard BCS paradigm. Firstly, the cavity-mediated electron-electron interactions are long range. This induces a novel, non-BCS-type of pairing mediated by on-shell, non-adiabatic photon fluctuations which signifaicantly enhances the pairing instability. Secondly, since this new pairing mechanism crucially depends on the population of the photons, this opens up an even more exciting prospect to exploit state-of-the-art engineering of the quantum states of light to control superconductivity. A naturally emerging question, which remains still open, is whether one can enhance superconductivity by feeding the cavity with certain quantum states of the photons. In this talk, I will describe our recent results in these directions obatined within a real-time field theoretic formulations.

Intertwining exotic quantum order and nontrivial topology is at the frontier of condensed matter physics. A charge density wave (CDW) like order with orbital currents has been proposed as a powerful resource for achieving the quantum anomalous Hall effect in topological materials and for the hidden phase in cuprate high-temperature superconductors. However, the experimental realization of such unconventional charge order is challenging. In this work we use high-resolution scanning tunnelling microscopy (STM) to discover an unconventional charge order in a kagome material KV3Sb5, with both a topological band structure and a superconducting ground state. Through both topography and spectroscopic imaging, we observe a robust 2×2 superlattice. Spectroscopically, an energy gap opens at the Fermi level, across which the 2×2 charge modulation exhibits an intensity reversal in real-space, signaling charge ordering. The strength of low-energy charge modulations further displays a clockwise or anticlockwise chiral anisotropy, which we demonstrate can be switched by an applied magnetic field. Theoretical analysis of our experiments suggests a highly unconventional CDW in the frustrated kagome lattice, which can not only lead to a large anomalous Hall effect, but also be a strong precursor of unconventional superconductivity.

The tuneability and control of quantum nanostructures in two-dimensional materials offer promising perspectives for their use in future electronics. It is hence necessary to analyze quantum transport in such nanostructures. Material properties such as a complex dispersion, topology, and charge carriers with multiple degrees of freedom, are appealing for novel device functionalities but complicate their theoretical description. Here, we study quantum tunnelling transport across a few-electron bilayer graphene quantum dot. We demonstrate how to uniquely identify single- and two-electron dot states' orbital, spin, and valley composition from differential conductance in a finite magnetic field. Furthermore, we show that the transport features manifest splittings in the dot's spin and valley multiplets induced by interactions and by the magnetic field (the latter being a consequence of bilayer graphene's Berry curvature). Our results teach about spin- and valley-dependent tunnelling mechanisms and will help to utilize bilayer graphene quantum dots, e.g., as spin and valley qubits.

The Density-Matrix Renormalisation Group (DMRG) has transformed the simulation of 1D lattice systems by utilising area law of entanglement to recursively truncate the exponentially large Hilbert space. However, attempts to generalise DMRG to continuous experimental systems have proved elusive. We introduce an intuitive and practical reformulation of DMRG to the continuum by using a flexible set of local basis functions that are subject to a continuity constraint. We benchmark our approach against Bethe Ansatz for interacting bosons in a box trap and demonstrate improved tuneable convergence over discretisation on a grid. We then apply our technique to find ground states of bosons in a sinusoidal trap, recovering known limits and showing a superfluid to Mott insulator transition in a shallow lattice.

Gross-Neveu-SO(3) is a new type universality class which relate to the research of two-dimensional spin-orbital magnets with strong exchange frustration. The key novelty of the critical point is that ordering only partially gaps out the spectrum: two out of three Dirac cones acquire a mass term. The recent theoretical study also give the prediction of the critical exponent of this universality class. Motivating by the theoretical study, we design a lattice model which don't suffer from the the negative sign problem and that falls into this universality class. By implementing the Quantum Monte Carlo method, we investigate the detail phase diagram of our lattice model and extract the critical exponent by finite size scaling analysis. We aim to confront our results to analytical estimates of the exponents.

Three dimensional magnetic systems promise significant opportunities for new physics, ranging from ultra-high domain wall velocities and geometry-induced magnetochirality effects, to 3D topological structures as well as 3D technological devices [1,2]. Experimentally, appropriate techniques are required to map both complex three-dimensional magnetic configurations, and the response to external excitations. For three-dimensional magnetic imaging, we have developed X-ray magnetic nanotomography [3], combining a new iterative reconstruction algorithm [4] with a dual rotation axis experimental setup, therefore providing access to the three-dimensional magnetic configuration at the nanoscale. In a first demonstration, we have determined the complex three-dimensional magnetic structure within the bulk of a micrometre-sized soft magnetic pillar and observed a magnetic configuration that consists of vortices and antivortices, as well as Bloch point singularities [3]. In addition to the static magnetic structure, the dynamic response of the 3D magnetic configuration to excitations is key to our understanding of both fundamental physics, and applications. With our recent development of X-ray magnetic laminography [5,6], it is now possible to determine the magnetisation dynamics of a three-dimensional magnetic system [5] with spatial and temporal resolutions of 50 nm and 70 ps, respectively. A final challenge concerns the identification of nanoscale topological objects within the complex reconstructed magnetic configurations. To address this, we have recently implemented calculations of the magnetic vorticity [7,8], that make possible the location and identification of 3D magnetic solitons, leading to the first observation of magnetic vortex rings [8]. These new experimental capabilities of X-ray magnetic imaging open the door to the elucidation of complex three-dimensional magnetic structures, and their dynamic behaviour. [1] Fernández-Pacheco et al., “Three-dimensional nanomagnetism” Nat. Comm. 8, 15756 (2017) [2] Donnelly and V. Scagnoli, “Imaging three-dimensional magnetic systems with X-rays” J. Phys. D: Cond. Matt. (2019). [3] Donnelly et al., “Three-dimensional magnetization structures revealed with X-ray vector nanotomography” Nature 547, 328 (2017). [4] Donnelly et al., “Tomographic reconstruction of a three-dimensional magnetization vector field” New Journal of Physics 20, 083009 (2018). [5] Donnelly et al., “Time-resolved imaging of three-dimensional nanoscale magnetization dynamics”, Nature Nanotechnology 15, 356 (2020). [6] Witte, et al., “From 2D STXM to 3D Imaging: Soft X-ray Laminography of Thin Specimens”, Nano Lett. 20, 1305 (2020). [7] Cooper, “Propagating magnetic vortex rings in ferromagnets.” PRL. 82, 1554 (1999). [8] Donnelly et al., “Experimental observation of vortex rings in a bulk magnet” Nat. Phys. 17, 316 (2021)

At strong repulsion, the triangular-lattice Hubbard model is described by s=1/2 spins with nearest-neighbor antiferromagnetic Heisenberg interactions and exhibits conventional 120° order. Using a combination of infinite density matrix renormalization group and exact diagonalization, we study the effect of the additional four-spin interactions naturally generated from the underlying Mott-insulator physics of electrons as the repulsion decreases. Although these interactions have historically been connected with a gapless ground state with emergent spinon Fermi surface, we find that at physically relevant parameters, they stabilize a chiral spin-liquid (CSL) of Kalmeyer-Laughlin (KL) type, clarifying observations in recent studies of the Hubbard model. We also present a self-consistent solution based on a mean-field rewriting of the four-spin interaction to obtain a Hamiltonian with similarities to the parent Hamiltonian of the KL state, providing a physical understanding for the origin of the CSL.

Recent years have seen a surge of interest in spin-orbit entangled Mott insulators, largely driven by the tantalizing prospect of realising the physics of Kitaev's celebrated honeycomb model. However, there are also other distinct exchange interactions that can be generated in such Mott insulators, which come with their own unique physics and intriguing properties. Here, we focus on off-diagonal symmetric exchange on the triangular and kagome lattices (with the honeycomb case having already been well-studied). In the classical limit the model, with an antiferromagnetic sign, leads on both lattices to classical spin liquid behavior. On the other hand, in the quantum spin-1/2 limit, quantum fluctuations drive both systems into ordered ground states. We will discuss various elements of these classical and quantum limits using a variety of analytical and numerical techniques, shedding light on these new exchange models within the realm of quantum magnetism.

Mechanical strain can generate a pseudo-magnetic field, and hence Landau levels (LL), for low energy excitations of quantum matter in two dimensions. We study the collective state of the fractionalised Majorana fermions arising from residual generic spin interactions in the central LL, where the projected Hamiltonian reflects the spin symmetries in intricate ways: emergent U(1) and particle-hole symmetries forbid any bilinear couplings, leading to an intrinsically strongly interacting system; also, they allow the definition of a filling fraction, which is fixed at 1/2. We argue that the resulting many-body state is gapless within our numerical accuracy, implying ultra-short-ranged spin correlations, while chirality correlators decay algebraically. This amounts to a Kitaev ‘nonFermi’ spin liquid, and shows that interacting Majorana Fermions can exhibit intricate behaviour akin to fractional quantum Hall physics in an insulating magnet.

Emergent excitation continua in frustrated magnets are a fingerprint of fractionalization, characteristic of quantum spin-liquid states. Recent evidence from Raman scattering for a coupling between such continua and lattice degrees of freedom in putative Kitaev magnets may provide insight into the nature of the fractionalized quasiparticles. Here, we report on the renormalization of optical phonons coupled to the underlying $\mathbb{Z}_{2}$ quantum spin-liquid. We show that phonon line-shapes acquire an asymmetry, observable in light scattering, and originating from two distinct sources, namely the dispersion of the Majorana continuum and the Fano effect. Moreover, we find that the phonon life-times increase with increasing temperature due to thermal blocking of available phase space. Finally, in contrast to low-energy probes, optical phonon renormalization is rather insensitive to thermally excited gauge fluxes and barely susceptible to external magnetic fields.

Quantum Spin Liquids have recently enjoyed renewed interest. This is partly driven by synergies with quantum information theory and by the experimental progress, which provides evidence for new material realizations, in particular in 2D van-der-Waals materials. The chemical versatility of this platform allows and requires the study of new probes in device geometries combining quantum spin liquids with, e.g., metals or semimetals. In this talk, I present a comprehensive study of electrical tunneling signatures of Kitaev quantum spin liquids in such heterostructures. I argue that momentum conserving tunneling setups, such as planar tunneling and the tunneling between quantum Hall edges are experimentally particularly suitable. In the second part, I will discuss the stability of the spin liquid state with respect to the coupling to an electronic bath. As an exemplary toy-model, I will demonstrate that a simple triangular Kondo-Heisenberg cluster impurity displays a topological phase and a trivial phase, which are separated by a deconfinement transition driven by the proliferation of monopole like gauge field excitations which is reminiscent of the confinement transition in 2D U(1) quantum spin liquids. [1] EJ König, MT Randeria, B Jäck; Physical Review Letters 125 (26), 267206 (2020) [2] EJ König, P Coleman, Y Komijani; arXiv:2002.12338 (2020)

We employ neural networks to find compressed representations of many-body quantum states. In this talk I focus on the application of this approach to quantum state tomography. I will report on state tomography on experimental data from a two-photon experiment and discuss the scalability of neural state tomography with convolutional neural networks. The most resource consuming task in this approach is the generation of Monte Carlo samples form the learned network representation. This task can potentially be accelerated by emulating the networks physically on neuromorphic hardware. I will report on the successful encoding of few-qubit entangled states on a neuromorphic chip.

Cavity spintronics is a rising field that manipulates the interaction of magnetic magnons and the photons inside a cavity, which benefits the advantages of the long lifetime and easy tunability properties of magnetic magnons. One promising route of this field is to bridge it with the quantum information science, which utilizes the entanglement of quasi-particles as a computing and information processing resource. A prior and crucial, but seldom studied question is how magnons and photons interplay inside the cavity to manifestate their entanglement properties. In this talk, I will first outline the recent developments in caivty spintronics and then present the antiferromagnetic magnon-magnon and magnon-photon entanglement inside a microwave cavity as well as their application potential in quantum information science. If time permits, I will further talk about the promising properties of van der Waals magnets as a platform to manipualte the entanglement of magnons.

Majorana bound states are zero-energy states predicted to emerge in topological superconductors and intense efforts seeking a definitive proof of their observation are still ongoing. A standard route to realize them involves antagonistic orders: a superconductor in proximity to a ferromagnet. Here we show this issue can be resolved using antiferromagnetic rather than ferromagnetic order. We propose to use a chain of antiferromagnetic skyrmions, in an otherwise collinear antiferromagnet, coupled to a bulk conventional superconductor as a novel platform capable of supporting Majorana bound states that are robust against disorder. Crucially, the collinear antiferromagnetic region neither suppresses superconductivity nor induces topological superconductivity, thus allowing for Majorana bound states localized at the ends of the chain. Our model introduces a new class of systems where topological superconductivity can be induced by editing antiferromagnetic textures rather than locally tuning material parameters, opening avenues for the conclusive observation of Majorana bound states.

Recent developments at the interface between quantum materials and photonics are opening novel avenues to engineer hidden phases of matter. Among these, quantum spin liquids provide paradigmatic examples of highly entangled quantum states of matter, hosting fractionalized excitations and emerging gauge fields. In this talk, I will propose to engineer these phases by exploiting the coupling of quantum magnets to the quantized light of an optical cavity. The interplay between the quantum fluctuations of the electromagnetic field and the strongly correlated electrons results in a tunable long-range, frustrating interaction between spins. This cavity-induced interaction robustly stabilizes spin liquid states, which occupy an extensive region in the phase diagram spanned by the range and strength of the tailored interaction. Remarkably, this occurs even in originally unfrustrated systems, as we showcase for the Heisenberg model on the square lattice. Finally, I will outline perspectives on how this implementation can be used for engineering further exotic states of matter, and for novel measurement protocols

Neural quantum states are a promising approach to studying many-body quantum physics. However, they face a major challenge when applied to lattice models: Neural networks struggle to converge to ground states with a nontrivial sign structure. Here, I present a neural network architecture with a simple, explicit, and interpretable phase ansatz, which can robustly represent such states and achieve state-of-the-art variational energies for both conventional and frustrated antiferromagnets. In the first case, the neural network correctly recovers the Marshall sign rule without any prior knowledge. For frustrated magnets, our approach uncovers low-energy states that exhibit the Marshall sign rule but does not reach the true ground state, which is expected to have a different sign structure. I discuss the possible origins of this "residual sign problem" as well as strategies for overcoming it, which may allow using neural quantum states for challenging spin liquid problems.

We combine quantum renormalization group approaches with deep artificial neural networks for the description of the real-time evolution in strongly disordered quantum matter. We find that this allows us to accurately compute the long-time coherent dynamics of large, many-body localized systems in non-perturbative regimes including the effects of many-body resonances. Concretely, we use this approach to describe the spatiotemporal buildup of many-body localized spin glass order in random Ising chains. We observe a fundamental difference to a non-interacting Anderson insulating Ising chain, where the order only develops over a finite spatial range. We further apply the approach to strongly disordered two-dimensional Ising models highlighting that our method can be used also for the description of the real-time dynamics of nonergodic quantum matter in a general context.

The development of non-Hermitian topological band theory has led to observations of novel topological phenomena in effectively classical, driven and dissipative systems. However, for open quantum many-body systems, the absence of a ground state presents a challenge to define robust signatures of non-Hermitian topology. We show that such a signature is provided by crossings in the time evolution of the entanglement spectrum. These crossings occur in quenches from the trivial to the topological phase of a driven-dissipative Kitaev chain that is described by a Markovian quantum master equation in Lindblad form. At the topological transition, which can be crossed either by changing parameters of the Hamiltonian of the system or by increasing the strength of dissipation, the time scale at which the first entanglement spectrum crossing occurs diverges with a dynamical critical exponent of $\epsilon = 1/2$. We corroborate these numerical findings with an exact analytical solution of the quench dynamics for a spectrally flat postquench Liouvillian. This exact solution suggests an interpretation of the topological quench dynamics as a fermion parity pump. Our work thus reveals signatures of non-Hermitian topology which are unique to quantum many-body systems and cannot be emulated in classical simulators of non-Hermitian wave physics.

Out of equilibrium properties of one-dimensional systems are a common ground of interest for a broad community, in view of their strong correlation and the enhanced role of the interactions. These systems are the perfect laboratory to investigate natural questions such as thermalization and transport, but their inherently strongly-interacting nature makes analytical results scarce. Integrable models stand out as one of the few examples of strongly interacting, yet analytically solvable, models. In this talk, I will provide a general introduction to the recently devised Generalized Hydrodynamics, namely a hydrodynamic method to exactly describe integrable systems in the presence of weak inhomogeneities and slow time dependence. In particular, I will emphasize the connection with cold atom experiments and the problem of thermalization.

In the first part of the talk I will introduce the basic idea of fractonic systems and show that the combination of charge and dipole conservation leads to an extensive fragmentation of the Hilbert space, which, in turn, can lead to a breakdown of thermalization. Considering a minimal model, we will find that the infinite temperature autocorrelation saturates to a finite value and show that for any finite range of interactions, the system exhibits nonthermal eigenstates appearing throughout the entire spectrum. We will explain this behavior as a consequence of the strong fragmentation of the Hilbert space into exponentially many invariant subspaces in the local Sz basis, arising from the interplay of dipole conservation and local interactions. However, when the system is not strongly but only weakly fragmented, it eventually reaches global equilibrium displaying subdiffusive decay of charge correlations. Towards the end of the talk, we will think about the experimental validation of these phenomena. It turns out the tilted one-dimensional Fermi-Hubbard model offers an extremely rich dynamical behavior, lying at the interface of Stark many-body localization and Hilbert-space fragmentation, and it is directly accessible in experiments with ultracold atoms in optical lattices.

Simulating the dynamics of quantum many-body systems, especially in spatial dimensions larger than one, is very challenging due to the exponentially large Hilbert space and the rapid growth of entanglement. We here present several examples where progress can be achieved by employing numerical linked cluster expansions (NLCEs), dynamical quantum typicality (DQT), as well as the combination of both these methods. While NLCEs yield the dynamics for infinitely large systems by carefully assembling the contributions of smaller subsystems embedded on the lattice, DQT relies on the fact that even a single random quantum state can accurately approximate ensemble averages. First, we demonstrate that NLCEs can boost typicality-based simulations of autocorrelation functions to study transport properties of quantum spin chains in the thermodynamic limit. Secondly, we consider quantum quenches in the paradigmatic two-dimensional transverse-field Ising model and show that NLCEs, combined with an efficient forward propagation of pure states, can yield converged results on time scales competitive to other state-of-the-art methods. We also provide a brief outlook how NLCEs might help to tackle the question of many-body localization even beyond the well-studied one-dimensional chain geometry.

We study the delocalization dynamics of interacting disordered hard-core bosons for quasi-1D and 2D geometries, with system sizes and timescales comparable to state-of-the-art experiments. The results are strikingly similar to the 1D case, with slow, subdiffusive dynamics featuring power-law decay. From the freezing of this decay we infer the critical disorder $W_c(L, d)$ as a function of length $L$ and width $d$. In the quasi-1D case $W_c$ has a finite large-$L$ limit at fixed $d$, which increases strongly with $d$. In the 2D case $W_c(L, L)$ grows with $L$. The results are consistent with the avalanche picture of the many-body localization transition.

We consider a clean quantum system subject to strong periodic driving. The existence of a dominant energy scale, $h_x^D$, can generate considerable structure in an effective description of a system which, in the absence of the drive, is non-integrable, interacting, and does not host localization. In particular, we uncover points of freezing in the space of drive parameters (frequency and amplitude). At those points, the dynamics is severely constrained due to the emergence of an almost exact local conserved quantity, which scars the entire Floquet spectrum by preventing the system from heating up ergodically, starting from any generic state, even though it delocalizes over an appropriate subspace. At large drive frequencies, where a naïve Magnus expansion would predict a vanishing effective (average) drive, we devise instead a strong-drive Magnus expansion in a moving frame. There, the emergent conservation law is reflected in the appearance of an `integrability' of an effective Hamiltonian. These results hold for a wide variety of Hamiltonians, including the Ising model in a transverse field in any dimension and for any form of Ising interactions. The phenomenon is also shown to be robust in the presence of two-body Heisenberg interactions with any arbitrary choice of couplings. Further, we construct a real-time perturbation theory which captures resonance phenomena where the conservation breaks down, giving way to unbounded heating. This opens a window on the low-frequency regime where the Magnus expansion fails.

The electromagnetic helicity of the free electromagnetic field and the static magnetic helicity are shown to be two different embodiments of the same physical quantity, the total helicity. The total helicity is the sum of two terms: A term that measures the difference between the number of left-handed and right-handed photons of the free field, and another term that measures the screwiness of the static magnetization density in matter. Each term is the manifestation of the total helicity in different frequency regimes: $\omega$ > 0 and $\omega$ = 0, respectively. This unification establishes the theoretical basis for studying the conversion between the two embodiments of total helicity upon light-matter interaction.

Superconductivity comes in a wide variety of incarnations including conventional s-wave, high-Tc d-wave, and topological p-wave. While these states are well defined theoretically, they are extremely difficult to distinguish experimentally: all superconductors have Cooper pairs, a Meissner effect, and a zero-resistance state, while any differences between states are subtle. I will give an overview of the experimental situation with a particular focus on how to find a bulk, three-dimensional topological superconductor, drawing on my own group's research on Sr2RuO4 and UTe2.

Since the discovery of topological phases of matter in solid-state materials, there has been great progress in engineering analogous effects for ultracold atoms and photonics systems. As these systems are highly flexible and tunable, this has opened up many new opportunities to realise topological models and to probe and exploit topological effects in new ways. In this overview talk, I will briefly introduce some of the recent advances in exploring topological quantum Hall physics with ultracold atoms and photons. This includes the implementation of approaches such as topological pumping and synthetic spatial dimensions, which even open up the way for the exploration of higher-dimensional topological physics.

Time-reversal symmetry (TRS) underpins many interesting phenomena in quantum mechanics, including certain topological phases such as topological insulators and the Haldane phase of quantum magnets. However, even if present at the microscopic level, TRS is effectively broken in the dynamics of open systems. In this talk, I will argue that certain topological phases are fundamentally unstable against coupling to their surroundings. System-environment interactions lead to the breaking of TRS in the sense that the system propagates irreversibly, and this same mechanism gives rise to processes that would be forbidden by TRS in an isolated system, thus compromising the protection of the phase in question. In particular, I will demonstrate that topological bound states at the edges of 1D topological systems protected by TRS are inevitably subject to decoherence. Analogously, in 2D systems this same mechanism compromises the quantized conductance of helical edge modes. Our results elucidate potential challenges in utilizing topological systems for quantum technologies, and may account for resistance measurements seen in experiments on quantum spin Hall systems. MM & Nigel Cooper, Nature Physics 16, 1181 (2020) MM & Nigel Cooper, arXiv:2009.14650

In chiral magnets a helical magnetic texture forms where the magnetization winds around a propagation vector ${q}$. We show theoretically that a magnetic field ${B}_{\perp}(t)\perp {q}$, which is spatially homogeneous but oscillating in time, induces a net rotation of the texture around ${q}$. This rotation is reminiscent of the motion of an Archimedean screw and is equivalent to a translation with velocity ${v}_{\text{screw}}$ parallel to ${q}$. Due to the coupling to a Goldstone mode, this non-linear effect arises for arbitrarily weak ${B}_{\perp}(t)\perp {q}$ with $v_{\text{screw}}\propto|{B}_{\perp}|^2$ as long as pinning by disorder is absent. The effect is resonantly enhanced when internal modes of the helix are excited and the sign of $v_{\text{screw}}$ can be controlled either by changing the frequency or the polarization of ${B}_{\perp}(t)$. The Archimedean screw can be used to transport spin and charge and thus the screwing motion is predicted to induce a voltage parallel to ${q}$. Using a combination of numerics and Floquet spin wave theory, we show that the helix becomes unstable upon increasing $B_{\perp}$ forming a `time quasicrystal', oscillating in space and time for moderately strong drive.

Coulomb spin liquids are topological magnetic states obeying an emergent Gauss’ law. Little distinction has been made between different kinds of Coulomb liquids. Here we show how a series of distinct Coulomb liquids, separated by T=0 phase transitions, can be generated straightforwardly by varying the constraints on a classical spin system. This leads to pair creation/annihilation, and coalescence, of topological defects of an underlying vector field. The latter makes higher-rank spin liquids, of recent interest in the context of fracton theories, with attendant multi-fold pinch points in the structure factor, appear naturally. New Coulomb liquids with an abundance of pinch points also arise. We thus establish a new and general route to uncovering exotic Coulomb liquids, via the manipulation of topological defects in momentum space.

Band topology is both constrained and enriched by the presence of symmetry. The importance of anti-unitary symmetries such as time reversal was recognized early on leading to the classification of topological band structures based on the ten-fold way. Since then, lattice point group and non- symmorphic symmetries have been seen to lead to a vast range of possible topologically nontrivial band structures many of which are realized in materials. We have shown that band topology is further enriched in many physically realizable instances where magnetic and lattice degrees of freedom are wholly or partially decoupled. The appropriate symmetry groups to describe general magnetic systems are the spin-space groups. We focus on magnon band topology where the theory of spin-space groups has its simplest realization and considered various types of coupling, including Heisenberg and Kitaev, revealing a symmetry-enforced proliferation of nodal points, lines, planes and volumes.

The last years have witnessed rapid progress in the topological characterization of out-of-equilibrium systems. We report on robust signatures of a new type of topology—the Euler class—in such a dynamical setting. The enigmatic invariant ($\xi$) falls outside conventional symmetry-eigenvalue indicated phases and, in simplest incarnation, is described by triples of bands that comprise a gapless pair featuring $2\xi$ stable band nodes, and a gapped band. These nodes host non-Abelian charges and can be further annihilated by converting their charge upon intricate braiding mechanisms, revealing that Euler class is a fragile topology. We theoretically study out-of-equilibrium response of the Euler class, which in turn makes the invariant experimentally observable. We demonstrate the quenching tecniques that have been recently established as a novel tool in probing topology in ultracold atomic systems result in stable monopole-antimonopole pairs in Euler class, which induce a linking of momentum-time trajectories. Our results provide a basis for exploring new topologies and their interplay with crystalline symmetries in optical lattices beyond paradigmatic Chern insulators.

A topological superconductor in one dimension can host Majorana zero modes at its edge. By driving the system periodically, so-called Pi modes (also named Floquet-Majoranas) can arise. These are topologically protected modes with an energy at the quasi-energy $\pi/T$ where T is the period of the drive. We consider the role of $\pi$ modes in the presence of long-ranged Coulomb interactions. We study a Cooper pair box made of two Josephson coupled superconducting topological quantum wires. Time-dependent gate voltages periodically drive the system. We investigate how to obtain and control $\pi$ modes and study their stability in the presence of interactions. We consider the limit where the charging energy is much larger than the Josephson energy. We find that periodic gate voltages result in a periodic phase modulation of the pairing term in the topological quantum wires. The phase modulation is by gauge transformation equivalent to a time-periodic chemical potential. In this setup all phases (trivial, Majorana zero mode, Majorana $\pi$ mode, both Majorana modes) are accessible. Taking into account a second order process via the bulk superconductor, we found an effective interaction term of the Hamiltonian. This interaction is of the form of non-local four body scattering in the wires. We discuss possible heating effects of the quasi-particle scattering. The presence of total two zero modes and two $\pi$ modes in the Floquet box qubit allows for topologically and parity protected single- and two qubit operations within one single box.

We consider the core problem of Coulomb interactions within fractionally filled Moiré flat bands and demonstrate that the dual description in terms of holes, which acquire a non-trivial hole-dispersion, provides key physical intuition and enables the use of standard perturbative techniques for this strongly correlated problem. We find that the single-hole dispersion has a profound impact on the phase diagram: in experimentally relevant examples such as ABC stacked trilayer and twisted bilayer graphene aligned with boron nitride, it leads to emergent Fermi liquid states at band filling fractions down to 1/3 and 2/3 respectively. Moreover, we predict both twisted bilayer graphene aligned with boron nitride and gate-tunable twisted double bilayer graphene to be versatile platforms for the realization of fractional Chern insulator states like spin-singlet Halperin states and spin polarized states in bands with Chern number C =1 and C = 2 at zero external magnetic fields.

Variational methods have proven to be excellent tools to approximate ground states of complex many body Hamiltonians. Generic tools like neural networks are extremely powerful, but their parameters are not necessarily physically motivated. Thus, an efficient parametrization of the wave-function can become challenging. In this letter we introduce a neural-network based variational ansatz that retains the flexibility of these generic methods while allowing for a tunability with respect to the relevant correlations governing the physics of the system. We illustrate the success of this approach on topological, long-range correlated and frustrated models. Additionally, we introduce compatible variational optimization methods for exploration of low-lying excited states without symmetries that preserve the interpretability of the ansatz.

Over recent decades, neural networks based machine learning technology has allowed huge improvements in image classifications/generations, natural language processing, and playing games. Inspired by those successes, Carleo and Troyer introduced a complex-valued restricted Boltzmann machine (RBM) — a primitive form of a neural network — for approximating quantum many-body states and showed that it accurately solves simple Hamiltonians, e.g., one and two-dimensional transverse-field Ising and the Heisenberg models. Subsequent studies observed that other neural network architectures also solve those Hamiltonian incredibly well combined with proper optimization algorithms. However, even for promising earlier results, it has also been found that neural quantum states still suffer several difficulties in solving highly frustrated systems, similar to conventional quantum Monte Carlo methods. Since frustrated Hamiltonians are non-stoquastic whose ground states have alternating signs in the computational basis, recent studies have investigated how complex sign structures of ground states are related to difficulties of neural quantum states. However, the connections revealed so far are obscure. In principle, neural quantum states can represent signs as well, and they indeed solve some non-stoquastic Hamiltonians. In this work, we clarify the relation between them by carefully classifying possible failure cases of neural quantum states. Most importantly, we find that complex RBMs can express ground states of a Hamiltonian phase connected to a stoquastic one. On the other hand, we also identify several new phases challenging for the RBM Ansatz, including non-topological robust non-stoquastic phases and stoquastic phases where complex RBMs do not learn ground states efficiently due to a sampling problem. Our results also suggest a kind of problem that near-term quantum devices can be superior over classical variational methods.