Long-time behavior of periodically driven isolated interacting lattice systems

Abstract

We study the dynamics of isolated interacting spin chains that are periodically driven by sudden quenches. Using full exact diagonalization of finite chains, we show that these systems exhibit three distinct regimes. For short driving periods, the Floquet Hamiltonian is well approximated by the time-averaged Hamiltonian, while for long periods the evolution operator exhibits properties of random matrices of a Circular Ensemble (CE). In-between, there is a crossover regime. Based on a finite-size scaling analysis and analytic arguments we argue that, for thermodynamically large systems and non-vanishing driving periods, the evolution operator always exhibits properties of CE random matrices. Consequently, the Floquet Hamiltonian is nonlocal and has multi-body interactions; and the driving leads to the equivalent of an infinite temperature state at long times. These results are connected to the breakdown of the Magnus expansion and are expected to hold beyond the specific lattice model considered.

11 pages, 8 figures, Published version

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• Inhomogeneous Floquet thermalization
• Second-order functional renormalization group approach to quantum wires out of equilibrium
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• Protecting Quantum Information via Many-Body Dynamical Localization
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• Absorption to Fluctuating Bunching States in Non-Unitary Boson Dynamics
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• Emergent topological phases and coexistence of gapless and spectral-localized Floquet quantum spin Hall states via electron-phonon interaction
• Integrable Floquet QFT: Elasticity and factorization under periodic driving
• Extended nonergodic regime and spin subdiffusion in disordered SU(2)-symmetric Floquet systems
• Controlling magnetic correlations in a driven Hubbard system far from half-filling
• Quench dynamics in the one-dimensional mass-imbalanced ionic Hubbard model
• Stable time rondeau crystals in dissipative many-body systems
• Deviations from random matrix entanglement statistics for kicked quantum chaotic spin-$1/2$ chains
• Bose-Einstein condensation in a frustrated triangular optical lattice
• Floquet Schrieffer-Wolff transform based on Sylvester equations
• Exploiting many-body localization for scalable variational quantum simulation
• The robustness condition for general disordered discrete time crystals, and subspace-thermal DTCs from phase transitions between different n-tuple DTCs
• Classical periodic trajectories and quantum scars in many-spin systems
• Tuning magnetic interactions with nonequilibrium optical phonon populations: a theoretical study
• Fermionic transport through a driven quantum point contact: breakdown of Floquet thermalization beyond a critical driving frequency
• Detecting prethermal Floquet phases of Rydberg atom arrays
• Discrete time crystals detected by time-translation twist
• Nonequilibrium phase transition in a driven-dissipative quantum antiferromagnet
• Electronic Mechanism that Quenches Field-Driven Heating as Illustrated with the Static Holstein Model
• Reciprocal Floquet thermalization in one-dimensional Rydberg atom array
• Prethermalization, shadowing breakdown, and the absence of Trotterization transition in quantum circuits
• Topological Phase Transitions and Edge-State Transfer in Time-Multiplexed Quantum Walks
• Resonant states of structured photonic time crystals
• On the commutator scaling in Hamiltonian simulation with multi-product formulas
• Information phases of partial projected ensembles generated from random quantum states and scrambling dynamics
• Long-time properties of generic Floquet systems are approximately periodic with the driving period
• Scaling of Loschmidt echo in boundary driven critical Z-3 Potts model
• Thermalization in parametrically driven coupled oscillators
• Floquet Gauge Pumps as Sensors for Spectral Degeneracies Protected by Symmetry or Topology
• Floquet engineering of topological phases protected by emergent symmetries under resonant drives
• Emergence of prethermal time quasicrystalline order in a quasiperiodically driven non-interacting spin chain
• Equilibration of Non-interacting Photons and Quantum Signatures of Chaos
• Long term behavior of the stirred vacuum on a Dirac chain: geometry blur and the random Slater ensemble
• Floquet thermalization by power-law induced permutation symmetry breaking
• Thouless Energy Across Many-Body Localization Transition in Floquet Systems
• Noise resilience of two-dimensional Floquet topological phases
• Trotter transition in BCS pairing dynamics
• Quantum Markov chain Monte Carlo method with programmable quantum simulators
• Onsager Reciprocal Relations for Charge and Spin Transport in Periodically Driven Systems
• Boundary Perturbation Effects in Quantum Systems with Conserved Energy and Continuous Symmetry
• Discrete time crystals in Bose-Einstein Condensates and symmetry-breaking edge in a simple two-mode theory
• Quantum fingerprints of self-organization in spin chains coupled to a Kuramoto model
• Chiral Instabilities in Driven-Dissipative Quantum Liquids
• Unpolarized prethermal discrete time crystal
• Engineering micromotion in Floquet prethermalization via space-time symmetries
• Characterizing the transition from topology to chaos in a kicked quantum system
• Emergence of caustics in dynamics of the Kitaev model
• Random-matrix approach to time-dependent forcing in many-body quantum systems
• Out-of-time-order correlators of nonlocal block-spin and random observables in integrable and nonintegrable spin chains
• Adiabatic and irreversible classical discrete time crystals
• Entanglement dynamics and ergodicity breaking in a quantum cellular automaton