Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54

Abstract

We study the out-of-equilibrium dynamics of the quantum cellular automaton Rule 54 using a time-channel approach. We exhibit a family of (non-equilibrium) product states for which we are able to describe exactly the full relaxation dynamics. We use this to prove that finite subsystems relax to a one-parameter family of Gibbs states. We also consider inhomogeneous quenches. Specifically, we show that when the two halves of the system are prepared in two different solvable states, finite subsystems at finite distance from the centre eventually relax to the non-equilibrium steady state (NESS) predicted by generalised hydrodynamics. To the best of our knowledge, this is the first exact description of the relaxation to a NESS in an interacting system and, therefore, the first independent confirmation of generalised hydrodynamics for an inhomogeneous quench.

arXiv comment47 pages, 3 figures; v2 accepted version

References in corpus (102)

• Theory of Bose-Einstein condensation in trapped gases
• The density-matrix renormalization group in the age of matrix product states
• Thermalization and its mechanism for generic isolated quantum systems
• Nonequilibrium dynamics of closed interacting quantum systems
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Real time evolution using the density matrix renormalization group
• Quantum many-body systems out of equilibrium
• Time-dependence of correlation functions following a quantum quench
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Quantum Inverse Scattering Method and Correlation Functions
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Nonequilibrium dynamical mean-field theory and its applications
• Operator Spreading in Random Unitary Circuits
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Quantum Quench in the Transverse Field Ising Chain
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Quantum Quenches in Extended Systems
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Theory of the phase transition in random unitary circuits with measurements
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Prethermalization
• Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
• Finite-temperature transport in one-dimensional quantum lattice models
• Critical properties of the measurement-induced transition in random quantum circuits
• Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
• Quasilocal charges in integrable lattice systems
• Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
• Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
• Solution of a minimal model for many-body quantum chaos
• Thermodynamics of the Anisotropic Spin-1/2 Heisenberg Chain and Related Quantum Chains
• Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
• "Light-cone" dynamics after quantum quenches in spin chains
• Prethermalization and universal dynamics in near-integrable quantum systems
• Nonequilibrium quantum dynamics and transport: from integrability to many-body localization
• Exact dynamics in dual-unitary quantum circuits
• The Quench Action
• Conformal field theory out of equilibrium: a review
• What is an integrable quench?
• Localization and Glassy Dynamics Of Many-Body Quantum Systems
• Postselection-free entanglement dynamics via spacetime duality
• Lecture notes on Generalised Hydrodynamics
• Matrix Product States for dynamical simulation of infinite chains
• Entanglement spreading in a minimal model of maximal many-body quantum chaos
• Unitary circuits of finite depth and infinite width from quantum channels
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Drude Weight for the Lieb-Liniger Bose Gas
• Quantum quench in the sine-Gordon model
• The entanglement membrane in chaotic many-body systems
• Ergodic and non-ergodic dual-unitary quantum circuits with arbitrary local Hilbert space dimension
• Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality
• Exact thermalization dynamics in the "Rule 54" Quantum Cellular Automaton
• Spacetime duality between localization transitions and measurement-induced transitions
• Particle-Time Duality in the Kicked Ising Chain I: The Dual Operator
• Particle-Time Duality in the Kicked Ising Chain II: Applications to the Spectrum
• Operator growth and eigenstate entanglement in an interacting integrable Floquet system
• Influence matrix approach to many-body Floquet dynamics
• Exact large-scale correlations in integrable systems out of equilibrium
• Quantum chaos in the Brownian SYK model with large finite $N$: OTOCs and tripartite information
• Dynamical free energy and the Loschmidt-echo for a class of quantum quenches in the Heisenberg spin chain
• Local pairing of Feynman histories in many-body Floquet models
• The Folded Spin-1/2 XXZ Model: I. Diagonalisation, Jamming, and Ground State Properties
• Tensor network techniques for the computation of dynamical observables in 1D quantum spin systems
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• A Random Unitary Circuit Model for Black Hole Evaporation
• Operator Dynamics in Brownian Quantum Circuit
• Non-analytic behavior of the Loschmidt echo in XXZ spin chains: exact results
• Random Matrix Spectral Form Factor of Dual-Unitary Quantum Circuits
• Many-body delocalisation as symmetry breaking
• Entanglement dynamics in Rule 54: Exact results and quasiparticle picture
• Connecting Entanglement in Time and Space: Improving the Folding Algorithm
• Computational power of one- and two-dimensional dual-unitary quantum circuits
• Integrable many-body quantum Floquet-Thouless pumps
• Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
• Quantum quenches and Generalized Gibbs Ensemble in a Bethe Ansatz solvable lattice model of interacting bosons
• Relaxation dynamics of local observables in integrable systems
• Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions
• Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
• Entanglement Barriers in Dual-Unitary Circuits
• The Folded Spin-1/2 XXZ Model: II. Thermodynamics and Hydrodynamics with a Minimal Set of Charges
• Quantum Quenches and Relaxation Dynamics in the Thermodynamic Limit
• Integrability of a deterministic cellular automaton driven by stochastic boundaries
• Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton
• Diffusion and operator entanglement spreading
• Transition from Quantum Chaos to Localization in Spin Chains
• Time-dependent matrix product ansatz for interacting reversible dynamics
• Statistics of the Spectral Form Factor in the Self-Dual Kicked Ising Model
• Exact matrix product decay modes of a boundary driven cellular automaton
• Coarse-grained dynamics of operator and state entanglement
• A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model
• Matrix product state of multi-time correlations
• Real-time dynamics in a strongly interacting bosonic hopping model: Global quenches and mapping to the XX chain
• Space-like dynamics in a reversible cellular automaton
• Real-Time Evolution in the Hubbard Model with Infinite Repulsion
• Two extensions of exact non-equilibrium steady states of a boundary driven cellular automaton
• How generalized hydrodynamics time evolution arises from a form factor expansion
• Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects
• Local correlations in dual-unitary kicked chains
• Strongly correlated non-equilibrium steady states with currents --- quantum and classical picture
• Non-Equilibrium Steady State of the Lieb-Liniger model: multiple-integral representation of the time evolved many-body wave-function

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• Random Quantum Circuits
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• Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
• Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
• Entanglement Negativity and Mutual Information after a Quantum Quench: Exact Link from Space-Time Duality
• Dynamics of charge fluctuations from asymmetric initial states
• Temporal Entanglement in Chaotic Quantum Circuits
• Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality
• A Yang-Baxter integrable cellular automaton with a four site update rule
• Growth of entanglement of generic states under dual-unitary dynamics
• Hierarchical generalization of dual unitarity
• Non-equilibrium dynamics of symmetry-resolved entanglement and entanglement asymmetry: Exact asymptotics in Rule 54
• Exact quench dynamics of the Floquet quantum East model at the deterministic point
• Magic Resources of the Heisenberg Picture
• Exact Spectral Statistics in Strongly Localised Circuits
• Real-Time Evolution in the Hubbard Model with Infinite Repulsion
• BBGKY Hierarchy and Generalised Hydrodynamics
• Global Quenches after Localised Perturbations
• Integrable deformations of superintegrable quantum circuits
• Integrable nonunitary quantum circuits
• Post-Quantum Quench Growth of Renyi Entropies in Low Dimensional Continuum Bosonic Systems
• An integrable spin chain with Hilbert space fragmentation and solvable real time dynamics
• Exactly solvable many-body dynamics from space-time duality
• Exact pre-transition effects in kinetically constrained circuits: dynamical fluctuations in the Floquet-East model
• Integrability breaking in the Rule 54 cellular automaton
• Reversible Cellular Automata as Integrable Interactions Round-a-Face: Deterministic, Stochastic, and Quantized
• Quantum and Classical Dynamics with Random Permutation Circuits
• Quench dynamics in lattices above one dimension: the free fermionic case
• Integrable spin chains and cellular automata with medium range interaction
• Operator spreading in quantum hardcore gases
• Efficient post-selection in light-cone correlations of monitored quantum circuits
• Growth of Rényi Entropies in Interacting Integrable Models and the Breakdown of the Quasiparticle Picture
• Thermodynamic symmetry resolved entanglement entropies in integrable systems
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