Exact quench dynamics of the Floquet quantum East model at the deterministic point

Abstract

We study the nonequilibrium dynamics of the Floquet quantum East model (a Trotterized version of the kinetically constrained quantum East spin chain) at its "deterministic point", where evolution is defined in terms of CNOT permutation gates. We solve exactly the thermalization dynamics for a broad class of initial product states by means of "space evolution". We prove: (i) the entanglement of a block of spins grows at most at one-half the maximal speed allowed by locality (i.e., half the speed of dual-unitary circuits); (ii) if the block of spins is initially prepared in a classical configuration, speed of entanglement is a quarter of the maximum; (iii) thermalization to the infinite temperature state is reached exactly in a time that scales with the size of the block.

arXiv comment19 pages, 3 figures

References in corpus (88)

• Probing many-body dynamics on a 51-atom quantum simulator
• Theoretical perspective on the glass transition and amorphous materials
• The large deviation approach to statistical mechanics
• Time-dependence of correlation functions following a quantum quench
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Quantum many-body scars
• Glassy dynamics of kinetically constrained models
• Operator Spreading in Random Unitary Circuits
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Quantum Zeno Effect and the Many-body Entanglement Transition
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Probing entanglement entropy via randomized measurements
• Measurement-driven entanglement transition in hybrid quantum circuits
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Quantum Many-Body Scars and Weak Breaking of Ergodicity
• Dynamics on the Way to Forming Glass: Bubbles in Space-time
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Unitary-projective entanglement dynamics
• Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
• Geometrical explanation and scaling of dynamical heterogeneities in glass forming systems
• Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians
• Controlling many-body dynamics with driven quantum scars in Rydberg atom arrays
• Critical properties of the measurement-induced transition in random quantum circuits
• Perspective: The Glass Transition
• Emergent SU(2) dynamics and perfect quantum many-body scars
• Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
• Periodic orbits, entanglement and quantum many-body scars in constrained models: matrix product state approach
• Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
• Solution of a minimal model for many-body quantum chaos
• Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
• Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
• Spectral statistics in spatially extended chaotic quantum many-body systems
• Exact dynamics in dual-unitary quantum circuits
• Postselection-free entanglement dynamics via spacetime duality
• Matrix Product States for dynamical simulation of infinite chains
• Entanglement spreading in a minimal model of maximal many-body quantum chaos
• Introduction to dynamical large deviations of Markov processes
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Many-body spin interactions and the ground state of a dense Rydberg lattice gas
• Aspects of non-equilibrium in classical and quantum systems: slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics
• Spectral statistics and many-body quantum chaos with conserved charge
• Dynamics of many-body localisation in a translation invariant quantum glass model
• Sub-ballistic growth of Rényi entropies due to diffusion
• The entanglement membrane in chaotic many-body systems
• Ergodic and non-ergodic dual-unitary quantum circuits with arbitrary local Hilbert space dimension
• Ergodicity and large deviations in physical systems with stochastic dynamics
• Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality
• Exact thermalization dynamics in the "Rule 54" Quantum Cellular Automaton
• Measurement Protocol for the Entanglement Spectrum of Cold Atoms
• Unitary $n$-designs via random quenches in atomic Hubbard and Spin models: Application to the measurement of Rényi entropies
• Probing scrambling using statistical correlations between randomized measurements
• Maximum velocity quantum circuits
• Influence matrix approach to many-body Floquet dynamics
• Many-body topological invariants from randomized measurements
• Quantum East model: localization, non-thermal eigenstates and slow dynamics
• Local pairing of Feynman histories in many-body Floquet models
• The Folded Spin-1/2 XXZ Model: I. Diagonalisation, Jamming, and Ground State Properties
• Formation of robust bound states of interacting microwave photons
• Tensor network techniques for the computation of dynamical observables in 1D quantum spin systems
• Efficient and feasible state tomography of quantum many-body systems
• Temporal entanglement, quasiparticles and the role of interactions
• Many-body delocalisation as symmetry breaking
• Random Matrix Spectral Form Factor of Dual-Unitary Quantum Circuits
• 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
• Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
• Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions
• Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54
• Entanglement Barriers in Dual-Unitary Circuits
• The Folded Spin-1/2 XXZ Model: II. Thermodynamics and Hydrodynamics with a Minimal Set of Charges
• Entanglement Negativity and Mutual Information after a Quantum Quench: Exact Link from Space-Time Duality
• Evidence of Kardar-Parisi-Zhang scaling on a digital quantum simulator
• Time Asymptotics and Entanglement Generation of Clifford Quantum Cellular Automata
• Hilbert space fragmentation and slow dynamics in particle-conserving quantum East models
• Superdiffusive Energy Transport in Kinetically Constrained Models
• Temporal Entanglement in Chaotic Quantum Circuits
• Statistics of the Spectral Form Factor in the Self-Dual Kicked Ising Model
• Dynamic facilitation theory: A statistical mechanics approach to dynamic arrest
• Distinct universality classes of diffusive transport from full counting statistics
• Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality
• Light cone tensor network and time evolution
• Barrier from chaos: operator entanglement dynamics of the reduced density matrix
• Localised Dynamics in the Floquet Quantum East Model
• Exact Spectral Statistics in Strongly Localised Circuits
• Thermalisation Dynamics and Spectral Statistics of Extended Systems with Thermalising Boundaries
• The Fredkin staircase: An integrable system with a finite-frequency Drude peak

Cited by in corpus (21)

• Non-equilibrium dynamics of charged dual-unitary circuits
• Quantum information spreading in generalised dual-unitary circuits
• The entanglement membrane in exactly solvable lattice models
• Zero-temperature entanglement membranes in quantum circuits
• Exactly solvable many-body dynamics from space-time duality
• Exact pre-transition effects in kinetically constrained circuits: dynamical fluctuations in the Floquet-East model
• Quantum and Classical Dynamics with Random Permutation Circuits
• Scalable simulation of non-equilibrium quantum dynamics via classically optimised unitary circuits
• Solvable entanglement dynamics in quantum circuits with generalized space-time duality
• Exact Hidden Markovian Dynamics in Quantum Circuits
• Dynamical heterogeneity and large deviations in the open quantum East glass model from tensor networks
• Anomalous transport in the kinetically constrained quantum East-West model
• Temporal Entanglement Barriers in Dual-Unitary Clifford Circuits with Measurements
• Exact results on the dynamics of the stochastic Floquet-East model
• State-dependent mobility edge in kinetically constrained models
• Entanglement dynamics and Page curves in random permutation circuits
• Graph theory and tunable slow dynamics in quantum East Hamiltonians
• Geometric constructions of generalized dual-unitary circuits from biunitarity
• Vanishing correlations in stochastic and bistochastic controlled circuits
• Exact large deviations and emergent long-range correlations in sequential quantum East circuits
• Weak-Memory Dynamics in Discrete Time