Constrained Many-body Dynamics

Quantum scarring is a phenomenon in quantum chaotic systems where there is an enhancement of the single-particle's wave function along classical, unstable orbits. Many-body quantum scars have recently been introduced to extend this notion to interacting quantum systems, which are characterised by the existence of many-body eigenstates with special properties, such as low entanglement and enhanced overlap with certain product states. The presence of scars explains the persistent periodic revivals observed in recent experiments on the dynamics of the kinetically-constrained Rydberg atom chain when it is quenched from an initial charge density wave state. We introduce a family of kinetically constrained coloured clock models which generalize the effective spin model describing the Rydberg atom chain. We show that clock models exhibit similar phenomenology of quantum many-body scars, including a special band of low-entangled states, revivals in the quench dynamics, and oscillations from easily preparable initial states. Nevertheless, we demonstrate that clock models are not equivalent to higher-spin extensions of the Rydberg chain, thus hinting at a new universality class of quantum-scarred models.

We study the motion of spinon excitations in a topological spin liquid (namely, Kitaev's toric code) in presence of thermally excited, static visons. The model maps onto a tight-binding model of charged particles in random pi-flux disorder. We demonstrate that the presence of visons curtails the ballistic propagation of spinons into a subdiffusive behaviour, in constrast with the case of continuous random fluxes that result in conventional diffusion. We investigate the origin of the phenomenon via effective models on a Bethe lattice and relate it to physical quantities of interest.

We present the non-linear spin-wave theory calculations of the dynamical response of an extended Kitaev-Heisenberg model for the parameters applicable to alphaRuCl3. We argue that large anisotropic terms of spin-orbit nature necessarily imply strong anharmonic coupling of magnons. Subsequently, the overlap of one- and two-magnon states must lead to broad spectral features in magnon spectrum. These are accompanied by a significant longitudinal component of the structure factor from the two-magnon states that are also broadened. We calculate magnon decay rates due to anharmonic coupling within a self-consistent approach and find our results for the dynamical structure factor to be in a good agreement with both exact diagonalization results for the same set of parameters and experiment.

Defect production for a ramp across a quantum critical point is described by the Kibble-Zurek mechanism, finding applications in diverse fields of physics. Here we focus on its generalization to a ramp across an exceptional point (EP) of a non-hermitian Hamiltonian. While adiabatic time evolution brings the system into an eigenstate of the final non-hermitian Hamiltonian, a PT-symmetric ramp to an EP or a passage from PT-symmetric to broken PT-symmetric states through an EP, produces a defect density scaling as $\tau^{-(d+z)\nu/(z\nu+1)}$ in terms of the usual critical exponents and $1/\tau$ the speed of the drive. Defect production is suppressed compared to the conventional hermitian case as the defect state can decay back to the ground state close to the EP; formally, only the part of the instantaneous excited state perpendicular to the ground state contributes to defect formation.

We study an integrable system that is reducible to free fermions by a Jordan-Wigner transformation which is subjected to a Fibonacci driving protocol based on two noncommuting Hamiltonians. In the high-frequency limit $\omega to \infty$, we show that the system reaches a nonequilibrium steady state, up to some small fluctuations which can be quantified. For each momentum the trajectory of the stroboscopically observed state lies between two concentric circles on the Bloch sphere; the circles represent the boundaries of the small fluctuations. The residual energy is found to oscillate in a quasiperiodic way between two values which correspond to the two Hamiltonians that define the Fibonacci protocol. These results can be understood in terms of an effective Hamiltonian which simulates the dynamics of the system in the high-frequency limit.

I shall discuss the ground state phase diagram and demonstrate the presence of a many-body localized (MBL) phase for an experimentally realizable one-dimensional (1D) constrained dipole boson model in the presence of an Aubry-Andre (AA) potential whose strength λ_0 can be tuned to precipitate an ergodic-MBL transition. I shall discuss the signature of such a transition in the quantum dynamics of the model by computing its response subsequent to a sudden quench of λ)0. I shall also show that the MBL and the ergodic phases can be clearly distinguished by study of post-quench dynamics and provide an estimate for minimal time up to which experiments need to track the response of the system to confirm the onset of the MBL phase. Shall suggest experiments which can test our theory.

We consider the quench dynamics of a two-dimensional (2D) constrained quantum dimer model and determine its rich dynamical phase diagram. By means of exact diagonalization on systems of sizes up to $8\times8$, we show that order parameters generically relax to their thermal expectation values. This allows us to interpret the far-from-equilibrium dynamics in terms of the underlying equilibrium phase transitions consisting of a BKT-transition between a columnar ordered valence bond solid (VBS) and a valence bond liquid (VBL), as well as a first order transition between a staggered VBS and the VBL. For quenches across the BKT transition, the Loschmidt rate develops non-analyticities at the zero-crossings of the order parameter, fixed by microscopic model parameters. By contrast, the relaxation time across the first order transition scales linearly with the average length scale of staggered domains in the initial state, preventing the formation of sharp kinks for infinitely large domains. Within the staggered VBS, some local observables even fail to thermalize as a result of the kinematic constraints of the quantum dimer model.

The Heisenberg antiferromagnet with uniform nearest-neighbour exchange on the pyrochlore lattice has a ground state that is macroscopically degenerate in the classical limit, and the degrees of freedom within the ground state manifold form an emergent gauge field. Weak exchange randomness lifts this ground state degeneracy and leads to spin glass freezing at a temperature scale set by the disorder. We discuss the low-energy excitations in this frozen state. Since the frozen state spontaneously breaks symmetry under global spin rotations, these excitations are expected to be Goldstone modes. In addition, to be low energy modes, they must be excitations of the emergent gauge field, which is distinguished from the one arising in spin ice materials because it has an intrinsic dynamics inherited from the precessional dynamics of Heisenberg spins. We show how the Halperin-Saslow theory of Goldstone modes in a spin glass must be modified to describe this constrained dynamics.

Local constraints on the Hilbert space of many-body systems lead to interesting ground state physics even when the non-constrained system is non interacting. We investigate a model of hard-core bosons with infinitely repulsive nearest- and next-nearest-neighbor interactions in one dimension, introduced by Fendley, Sengupta and Sachdev in Phys. Rev. B 69, 075106 (2004). Using various numerical methods we show how an intermediate gapless phase separates a crystalline and a disordered phase. We base our analysis on a variety of diagnostics, including entanglement measures, correlation functions, and spectral properties. We show that the gapless-to-solid transition is continuous, with dynamical critical exponent larger than 1 and that finite size scaling at the gapless-to-liquid transition is consistent with Berezinskii-Kosterlitz-Thouless universal behaviour.

Quantum link models are extensions of Wilson-type lattice gauge theories which realize exact gauge invariance with finite-dimensional Hilbert spaces. Quantum link models not only reproduce the standard features of Wilson's lattice gauge theories, but also host new phenomena such as crystalline confined phases. We study the non-equilibrium quench dynamics for two representative cases, $U(1)$ quantum link models in (1+1)d and (2+1)d, through the lens of dynamical quantum phase transitions. Finally, we discuss the connection to the high-energy perspective and the experimental feasibility to observe the discussed phenomena in recent quantum simulator settings such as trapped ions, ultra-cold atoms, and Rydberg atoms.

We show that long-range ferromagnetic interactions in quantum spin chains can induce spatial quasi-localization of topological magnetic defects, i.e., domain-walls, even in the absence of quenched disorder. By means of matrix-product-states numerical techniques, we study the non-equilibrium evolution of initial states with one or more domain-walls under the effect of a transverse field in variable-range quantum Ising chains. Upon increasing the range of these interactions, we demonstrate the occurrence of a sharp transition characterized by the suppression of spatial diffusion of the magnetic defects during the accessible time scale: the excess energy density remains localized around the initial positions of the domain-walls. This quasi-localization is accurately reproduced by an effective semiclassical model, which elucidates the crucial role that long-range interactions play in this phenomenon. These predictions can be tested in current experiments with trapped ions.

We investigate the out-of-equilibrium dynamics of non-interacting fermions in a generic mesocopic disordered grain, by combining numerical results with analytical considerations. We focus on the distribution of work, performed during quenches in different – orthogonal or unitary – random matrix ensembles, for a Fermi sea initial state. We analyze how this work statistics reflects the structure of particle-hole excitations, in particular, the level statistics of the underlying matrix ensemble. We demonstrate that the initial Fermi sea shows a diffusive broadening during the quench, with the quench-velocity dependent diffusion coefficient reflecting the different level repulsion in the two ensembles. Turning to the full distribution of work, we find clear fingerprints of the rigidity of energy levels in the probability density function for slow quenches. Remarkably, the most important features of the work statistics can be captured by a classical Markovian description, taking into account only nearest neighbor level transitions of the fermions. Our results could be experimentally accessible by calorimetric measurements in mesoscopic settings.

In this work we show how localization of excitation can emerge in non-disordered non-integrable systems, thus leading to an unexpected suppression of information scrambling in non-equilibrium setups.This violates the common belief according to which any initial macroscopic inhomogeneity in extended many-body systems is smoothed out by the time evolution through the activation of transport processes, that, can be ballistic or diffusive. In particular, we demonstrate this in the quantum Ising chain with transverse and longitudinal magnetic fields in the paradigmatic case of the evolution of domain-wall states. We perform extensive numerical simulations of the dynamics which turn out to be in excellent agreement with an effective analytical description valid within both weak and strong confinement regimes. Our results show that the energy flow from" hot" to" cold" regions of the chain is suppressed for all accessible times.

We study Floquet topological transition in irradiated graphene when the polarization of incident light changes randomly with time. We numerically confirm that the noise-averaged time-evolution operator approaches a steady value in the limit of exact Trotter decomposition of the whole period during which incident light has a different polarization at each interval of the decomposition. This steady limit is found to coincide with the time-evolution operator calculated from the noise-averaged Hamiltonian. We observe that at the six corners (Dirac/K point) of the hexagonal Brillouin zone of graphene random Gaussian noise strongly modifies the phase band structure induced by circularly polarized light, whereas in the zone center ($\Gamma$ point) even a strong noise is not able to do the same. This can be understood by analyzing the deterministic noise-averaged Hamiltonian, which has a different Fourier structure as well as a lower number of symmetries compared to the noise-free one. In one-dimensional systems noise is found to renormalize only the drive amplitude.

We investigate the dynamics of quantum entanglement after a global quench in systems that have diffusive transport of conserved quantities (energy, charge, etc.). We uncover a qualitative difference between the behavior of the von Neumann entropy and higher Rényi entropies and argue that the latter generically grow sub-ballistically. We provide strong evidence for this in a U(1)-symmetric random circuit model and interpret our results as a consequence of rare events due to local quantum fluctuations of the conserved density. We find numerically the same sub-ballistic growth of Rényi entropies in a paradigmatic non-integrable spin chain, where energy is the sole conserved quantity. We also discuss the late-time behavior of the second Rényi entropy and show that it exhibits hydrodynamic tails with three distinct power laws appearing for different classes of initial states.

Fracton phases are characterized by excitations that exhibit restricted mobility. These mobility constraints are thought to be related to the conservation of the dipole moment associated to a given charge quantum number. Motivated by recent results on random unitary circuits [2], we study one dimensional spin-1/2 and spin-1 Hamiltonian systems that conserve a U(1)-charge and its associated dipole moment. Our goal is to study the structure of the Hilbert space and the effects of these conservation laws on the dynamics, for example localization, and compare our results to those previously obtained for random unitary circuits. [2] S. Pai, M. Pretko and R. M. Nandkishore. arXiv:1807.09776 [cond-mat.stat-mech]

We numerically study many body chaos near the thermal phase transition of self-interacting relativistic scalar field theory in the classical statistical approximation. We find ballistic spreading and exponential growth of chaos even when the spectral function exhibits critical slowing down and diffusive transport. Both the Lyapunov exponent and the butterfly velocity exhibit a maximum near the phase transition and the former shows algebraic behaviour on approach to the non-interacting limit in analogy to order-to-chaos transitions. Furthermore, run-to-run fluctuations exhibit a self-similar behaviour in accordance with the (1+1)D KPZ universality class. We put our results into perspective with the low-energy excitations obtained from the spectral function. Our method can be used to study other field theories in regimes dominated by classical statistical fluctuations.

Gauge theories are the cornerstone of our understanding of fundamental interactions among particles. Their properties are often probed in dynamical experiments, such as those performed at ion colliders and high-intensity laser facilities. Describing the dynamics of these strongly coupled systems is a formidable challenge for classical computers, and represents one of the key target for quantum simulation and quantum computing approaches to particle physics phenomena. However, despite an intense theoretical effort and remarkable proof-of-principle experiments, the large-scale quantum simulation of a gauge theory stands as an open quest. Here, we show how recent experiments performed in Rydberg atom chains naturally realize the real-time dynamics of a lattice gauge theory at system sizes at the boundary of classical computational methods. We prove that the constrained Hamiltonian dynamics induced by strong Rydberg interactions maps exactly onto the one of a $U(1)$ lattice gauge theory. Building on this correspondence, we show that the recently observed anomalously slow dynamics corresponds to a string-inversion mechanism, reminiscent of the string-breaking typically observed in gauge theories. This underlies the generality of this slow dynamics, which we illustrate in the context of one-dimensional quantum electrodynamics on the lattice. Within the same platform, we propose a set of experiments that generically show long-lived oscillations, including the evolution of particle-antiparticle pairs. Our work sets the quantum simulation state-of-the-art for lattice gauge theories at 51 qubits, and connects the recently observed slow dynamics in atomic systems to epitome particle physics phenomena.

Motivated by recent experimental observations of coherent many-body revivals in a constrained Rydberg atom chain, we construct a weak exponentially local deformation of the Rydberg blockade Hamiltonian, which makes the quantum revivals almost exact. Our analysis suggests the existence of an underlying non-integrable Hamiltonian which supports an emergent SU(2)-spin dynamics within a small subspace of the many-body Hilbert space. This indicates the presence of atypical, nonergodic energy eigenstates --- quantum many-body scars. Our results offers a route to enhance coherent many-body revivals, which could be naturally implemented in atomic lattice setups.

Almost a century ago, string states — complex bound states of magnetic excitations — were predicted to exist in one-dimensional quantum magnets1. However, despite many theoretical studies, the experimental realization and identification of string states in a condensed-matter system have yet to be achieved. Here we use high-resolution terahertz spectroscopy to resolve string states in the antiferromagnetic Heisenberg–Ising chain SrCo2V2O8 in strong longitudinal magnetic fields. In the field-induced quantum-critical regime, we identify strings and fractional magnetic excitations that are accurately described by the Bethe ansatz. Close to quantum criticality, the string excitations govern the quantum spin dynamics, whereas the fractional excitations, which are dominant at low energies, reflect the antiferromagnetic quantum fluctuations.

Using the Kanamori's approach to correlations in narrow band metals, we formulate a novel diagrammatic technique applicable to a large number of quantum magnets including singlet dimer systems, strong single-ion magnets, and the Ising spin model in a transverse applied field. The local constraint on the number of excitations per site/dimer is taken into account via exact solution of the two particle problem. The subsequent diagrammatic expansion is performed in 1/z, z being the coordination number. The developed approach is applied to the above mentioned models at zero and finite temperatures. Apart from a few standard results we derive a temperature-dependent band renormalization in triplon bands.

The time-dependent variational principle (TDVP) is a general method for approximating the full many-body quantum dynamics with a semiclassical dynamics on a restricted part of the Hilbert space. I will discuss how this semiclassical evolution can be quantized to obtain a stochastic motion on the semiclassical manifold which precisely describes the full many-body quantum state. The derived method interpolates between the phase-space methods and the matrix product state methods (e.g., TEBD or TDVP) and provides further insight into the connection between entanglement growth and the problem of diverging trajectories. I will also present a formulation of the TDVP for integrable systems.