Solution of a minimal model for many-body quantum chaos

Abstract

We solve a minimal model for quantum chaos in a spatially extended many-body system. It consists of a chain of sites with nearest-neighbour coupling under Floquet time evolution. Quantum states at each site span a $q$-dimensional Hilbert space and time evolution for a pair of sites is generated by a $q^2\times q^2$ random unitary matrix. The Floquet operator is specified by a quantum circuit of depth two, in which each site is coupled to its neighbour on one side during the first half of the evolution period, and to its neighbour on the other side during the second half of the period. We show how dynamical behaviour averaged over realisations of the random matrices can be evaluated using diagrammatic techniques, and how this approach leads to exact expressions in the large-$q$ limit. We give results for the spectral form factor, relaxation of local observables, bipartite entanglement growth and operator spreading.

Accepted in PRX

References in corpus (6)

• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
• Spectral statistics in spatially extended chaotic quantum many-body systems
• Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
• Many-body quantum chaos: Analytic connection to random matrix theory
• Effective field theory approach to many-body localization

Cited by in corpus (262)

• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Measurement-driven entanglement transition in hybrid quantum circuits
• Measurement-induced criticality in random quantum circuits
• Unitary-projective entanglement dynamics
• Quantum chaos challenges many-body localization
• Critical properties of the measurement-induced transition in random quantum circuits
• A Universal Operator Growth Hypothesis
• Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
• Entanglement in a fermion chain under continuous monitoring
• Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
• Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
• Emergent statistical mechanics of entanglement in random unitary circuits
• Entanglement phase transitions in measurement-only dynamics
• Entanglement Transitions from Holographic Random Tensor Networks
• Exact dynamics in dual-unitary quantum circuits
• Entanglement spreading in a minimal model of maximal many-body quantum chaos
• Self-Organized Error Correction in Random Unitary Circuits with Measurement
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Entanglement and purification transitions in non-Hermitian quantum mechanics
• Spectral statistics and many-body quantum chaos with conserved charge
• Localization in fractonic random circuits
• The entanglement membrane in chaotic many-body systems
• Ergodic and non-ergodic dual-unitary quantum circuits with arbitrary local Hilbert space dimension
• Introduction to Haar Measure Tools in Quantum Information: A Beginner's Tutorial
• Many-Body Localization in the Age of Classical Computing
• Quasiparticle dynamics of symmetry resolved entanglement after a quench: the examples of conformal field theories and free fermions
• Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits
• Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions
• Scrambling in Random Unitary Circuits: Exact Results
• Exact thermalization dynamics in the "Rule 54" Quantum Cellular Automaton
• Quasilocalized dynamics from confinement of quantum excitations
• Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
• Algebraic Theory of Quantum Synchronization and Limit Cycles under Dissipation
• Many-body physics in the NISQ era: quantum programming a discrete time crystal
• Maximum velocity quantum circuits
• Influence matrix approach to many-body Floquet dynamics
• Measurement-induced phase transitions in $(d+1)$-dimensional stabilizer circuits
• Measurement-induced criticality and entanglement clusters: a study of 1D and 2D Clifford circuits
• Symmetry restoration and quantum Mpemba effect in symmetric random circuits
• Slow quantum thermalization and many-body revivals from mixed phase space
• Multipole conservation laws and subdiffusion in any dimension
• Quantum chaos in the Brownian SYK model with large finite $N$: OTOCs and tripartite information
• Local pairing of Feynman histories in many-body Floquet models
• Open Quantum Symmetric Simple Exclusion Process
• From dual-unitary to quantum Bernoulli circuits: Role of the entangling power in constructing a quantum ergodic hierarchy
• Mean-field entanglement transitions in random tree tensor networks
• Entanglement Oscillations near a Quantum Critical Point
• Probing many-body quantum chaos with quantum simulators
• Eigenstate Correlations, Thermalization and the Butterfly Effect
• Quantum information scrambling after a quantum quench
• A Random Unitary Circuit Model for Black Hole Evaporation
• Spectral statistics in constrained many-body quantum chaotic systems
• Thermofield dynamics: Quantum Chaos versus Decoherence
• Many-body delocalisation as symmetry breaking
• Origin of the slow growth of entanglement entropy in long-range interacting spin systems
• Scrambling is Necessary but Not Sufficient for Chaos
• Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
• Random Lindblad Dynamics
• Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
• Model of level statistics for disordered interacting quantum many-body systems
• Subdiffusion and many-body quantum chaos with kinetic constraints
• Quantum coding with low-depth random circuits
• Entanglement production and information scrambling in a noisy spin system
• Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions
• Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
• A statistical mechanism for operator growth
• Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54
• Spectral and Steady-State Properties of Random Liouvillians
• Entanglement Barriers in Dual-Unitary Circuits
• Scrambling Transition in a Radiative Random Unitary Circuit
• Temperature dependence of butterfly effect in a classical many-body system
• Entanglement revivals as a probe of scrambling in finite quantum systems
• Equilibrium Fluctuations in Maximally Noisy Extended Quantum Systems
• Entanglement Negativity and Mutual Information after a Quantum Quench: Exact Link from Space-Time Duality
• Noisy Coupled Qubits: Operator Spreading and the Fredrickson-Andersen Model
• Maximal entanglement velocity implies dual unitarity
• A cavity-QED simulator of slow and fast scrambling
• Chaos and Ergodicity in Extended Quantum Systems with Noisy Driving
• Random Matrix Spectral Form Factor in Kicked Interacting Fermionic Chains
• Dynamics of charge fluctuations from asymmetric initial states
• Entanglement distribution in the Quantum Symmetric Simple Exclusion Process
• Spectral Lyapunov exponents in chaotic and localized many-body quantum systems
• Correlations and commuting transfer matrices in integrable unitary circuits
• Many-body quantum chaos and emergence of Ginibre ensemble
• Monitoring Quantum Simulators via Quantum Non-Demolition Couplings to Atomic Clock Qubits
• Temporal Entanglement in Chaotic Quantum Circuits
• Scaling of temporal entanglement in proximity to integrability
• Transition from Quantum Chaos to Localization in Spin Chains
• Semiclassical roots of universality in many-body quantum chaos
• From CFTs to theories with Bondi-Metzner-Sachs symmetries: Complexity and out-of-time-ordered correlators
• Numerically Probing the Universal Operator Growth Hypothesis
• Operator Spreading in Quantum Maps
• Strong ergodicity breaking due to local constraints in a quantum system
• From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics
• Statistics of the Spectral Form Factor in the Self-Dual Kicked Ising Model
• Exact dynamics in dual-unitary quantum circuits with projective measurements
• Markovian Entanglement Dynamics under Locally Scrambled Quantum Evolution
• Self-averaging in many-body quantum systems out of equilibrium: Chaotic systems
• Test of Eigenstate Thermalization Hypothesis Based on Local Random Matrix Theory
• Many Body Quantum Chaos and Dual Unitarity Round-a-Face
• Dynamics of Fluctuations in Quantum Simple Exclusion Processes
• Eigenstate thermalization and rotational invariance in ergodic quantum systems
• Classification of Matrix-Product Unitaries with Symmetries
• Fastest local entanglement scrambler, multistage thermalization, and a non-Hermitian phantom
• Measuring Spectral Form Factor in Many-Body Chaotic and Localized Phases of Quantum Processors
• Measurement-induced phases of matter require feedback
• Simulation of quantum many-body dynamics with Tensor Processing Units: Floquet prethermalization
• Signatures of Chaos in Non-integrable Models of Quantum Field Theory
• Non-equilibrium dynamics of charged dual-unitary circuits
• Exact solution of the Floquet-PXP cellular automaton
• Growth of entanglement of generic states under dual-unitary dynamics
• Solvable non-Hermitian skin effect in many-body unitary dynamics
• Measurement induced entanglement transition in two dimensional shallow circuit
• Evolution of entanglement spectra under generic quantum dynamics
• Decodable hybrid dynamics of open quantum systems with Z_2 symmetry
• Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains
• Construction and local equivalence of dual-unitary operators: from dynamical maps to quantum combinatorial designs
• From Dual Unitarity to Generic Quantum Operator Spreading
• Entanglement measures of bipartite quantum gates and their thermalization under arbitrary interaction strength
• Entanglement growth after inhomogenous quenches
• Dynamical quantum ergodicity from energy level statistics
• Diffusive scaling of Rényi entanglement entropy
• Entanglement Dynamics after a Quench in Ising Field Theory: A Branch Point Twist Field Approach
• Topological lower bound on quantum chaos by entanglement growth
• Statistics of phase space localization measures and quantum chaos in the kicked top model
• Hilbert space fragmentation produces a "fracton Casimir effect"
• Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits
• Barrier from chaos: operator entanglement dynamics of the reduced density matrix
• Spectral form factor in a minimal bosonic model of many-body quantum chaos
• Exact quench dynamics of the Floquet quantum East model at the deterministic point
• Efficient Large-Scale Many-Body Quantum Dynamics via Local-Information Time Evolution
• Circuits of space and time quantum channels
• Exact Spectral Statistics in Strongly Localised Circuits
• Magic Resources of the Heisenberg Picture
• Height-conserving quantum dimer models
• Can the Macroscopic Fluctuation Theory be Quantized?
• Quantum information spreading in generalised dual-unitary circuits
• Krylov complexity and Trotter transitions in unitary circuit dynamics
• Absence of measurement-induced entanglement transition due to feedback-induced skin effect
• Space-like dynamics in a reversible cellular automaton
• Growth of genuine multipartite entanglement in random unitary circuits
• Out-of-Time-Order Correlation as a Witness for Topological Phase Transitions
• Emergence of many-body quantum chaos via spontaneous breaking of unitarity
• Three-fold way of entanglement dynamics in monitored quantum circuits
• Quantifying quantum chaos through microcanonical distributions of entanglement
• Universal fluctuations around typicality for quantum ergodic systems
• From observations to complexity of quantum states via unsupervised learning
• Universal Dephasing Mechanism of Many-Body Quantum Chaos
• Real-time correlators in chaotic quantum many-body systems
• Macroscopic effects of localised measurements in jammed states of quantum spin chains
• BROTOCs and Quantum Information Scrambling at Finite Temperature
• Eigenstate correlations, the eigenstate thermalization hypothesis, and quantum information dynamics in chaotic many-body quantum systems
• Butterfly Effect and Spatial Structure of Information Spreading in a Chaotic Cellular Automaton
• From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics
• Sachdev-Ye-Kitaev circuits for braiding and charging Majorana zero modes
• Exact universal bounds on quantum dynamics and fast scrambling
• Phantom relaxation rate of the average purity evolution in random circuits due to Jordan non-Hermitian skin effect and magic sums
• Many-body chaos near a thermal phase transition
• Integrable Quantum Circuits from the Star-Triangle Relation
• The Floquet Baxterisation
• Topological Defects in Floquet Circuits
• Corrections to diffusion in interacting quantum systems
• Boundary Chaos: Exact Entanglement Dynamics
• Operator dynamics in Floquet many-body systems
• Entanglement front generated by an impurity travelling in an isolated many-body quantum system
• Coarse-grained Entanglement and Operator Growth in Anomalous 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
• Multi-Region Entanglement in Locally Scrambled Quantum Dynamics
• Mixing and localisation in random time-periodic quantum circuits of Clifford unitaries
• Quantum-classical correspondence of strongly chaotic many-body spin models
• Universal out-of-equilibrium dynamics of 1D critical quantum systems perturbed by noise coupled to energy
• Integrable spin chains and cellular automata with medium range interaction
• Absence of localization in two-dimensional Clifford circuits
• Structured volume-law entanglement in an interacting, monitored Majorana spin liquid
• Unitary k-designs from random number-conserving quantum circuits
• Universal late-time dynamics in isolated one-dimensional statistical systems with topological excitations
• Quantum and Classical Dynamics with Random Permutation Circuits
• Two-step relaxation in local many-body Floquet systems
• Many-body systems with random spatially local interactions
• Asymmetric butterfly velocities in 2-local Hamiltonians
• Exact solution of the Rule 150 reversible cellular automaton
• Solvable entanglement dynamics in quantum circuits with generalized space-time duality
• Purity decay rate in random circuits with different configurations of gates
• Spacetime picture for entanglement generation in noisy fermion chains
• Classical route to ergodicity and scarring in collective quantum systems
• Slow thermalization and subdiffusion in $U(1)$ conserving Floquet random circuits
• Single-Particle Universality of the Many-Body Spectral Form Factor
• Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor
• Quantum eigenstates from classical Gibbs distributions
• Symmetry breaking in chaotic many-body quantum systems at finite temperature
• Quantum algorithm for evaluating operator size with Bell measurements
• Operator Spreading in the Memory Matrix Formalism
• Fundamental charges for dual-unitary circuits
• Open-system spin transport and operator weight dissipation in spin chains
• Quantum complexity phase transitions in monitored random circuits
• Many-body quantum chaos in mixtures of multiple species
• Temporal fluctuations of correlators in integrable and chaotic quantum systems
• Operator spreading in quantum hardcore gases
• Hamiltonian Dynamics of a Sum of Interacting Random Matrices
• Random matrix universality in dynamical correlation functions at late times
• Free fermions under adaptive quantum dynamics
• Integrability breaking and bound states in Google's decorated XXZ circuits
• Fisher zeroes and the fluctuations of the spectral form factor of chaotic systems
• Quantum reservoir probing: an inverse paradigm of quantum reservoir computing for exploring quantum many-body physics
• Symmetry protected entanglement in random mixed states
• Entanglement transition through Hilbert-space localization
• Information Flow in Non-Unitary Quantum Cellular Automata
• Measurement-Induced Phase Transition in State Estimation of Chaotic Systems and the Directed Polymer
• Exact spectral form factors of non-interacting fermions with Dyson statistics
• Universal distributions of overlaps from generic dynamics in quantum many-body systems
• Dilution of error in digital Hamiltonian simulation
• Structural Stability Hypothesis of Dual Unitary Quantum Chaos
• Characterizing quantum chaoticity of kicked spin chains
• Efficient post-selection in light-cone correlations of monitored quantum circuits
• Dynamics of entanglement fluctuations and quantum Mpemba effect in the $\nu =1$ QSSEP model
• No-resonance conditions, random matrices, and quantum chaotic models
• Purification Dynamics in a Continuous-time Hybrid Quantum Circuit Model
• Slow melting of a disordered quantum crystal
• Exact quench dynamics of symmetry resolved entanglement in a free fermion chain
• Tensor product random matrix theory
• Late-time ensembles of quantum states in quantum chaotic systems
• More on the Operator Space Entanglement (OSE): Rényi OSE, revivals, and integrability breaking
• Random non-Hermitian action theory for stochastic quantum dynamics: from canonical to path integral quantization
• Solvable Quantum Circuits in Tree+1 Dimensions
• Traveling discontinuity at the quantum butterfly front
• Dual-unitary shadow tomography
• Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits
• Entanglement patterns of quantum chaotic Hamiltonians with a scalar U(1) charge
• Spectral Statistics of Non-Hermitian Matrices and Dissipative Quantum Chaos
• Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling
• Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions
• Entanglement of bosonic systems under monitored evolution
• Statistics of the Random Matrix Spectral Form Factor
• Random Permutation Circuits Beyond Qubits are Quantum Chaotic
• Kicked-Ising Quantum Battery
• Deviations from random matrix entanglement statistics for kicked quantum chaotic spin-$1/2$ chains
• Hierarchical analytical approach to universal spectral correlations in Brownian Quantum Chaos
• Field theory of charge sharpening in symmetric monitored quantum circuits
• Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics
• Spectral anomalies and broken symmetries in maximally chaotic quantum maps
• Discrete time crystals detected by time-translation twist
• Dynamics of charge-imbalance-resolved entanglement negativity after a quench in a free-fermion model
• Hierarchy of timescales in a disordered spin-$1/2$ XX ladder
• Dynamics of Loschmidt echoes from operator growth in noisy quantum many-body systems
• Circular Rosenzweig-Porter random matrix ensemble
• Ensemble-averaged mean-field many-body level density: an indicator of integrable versus chaotic single-particle dynamics
• Anticoncentration in Clifford Circuits and Beyond: From Random Tensor Networks to Pseudo-Magic States
• Boundary Chaos: Spectral Form Factor
• Domain-wall melting in all-to-all QSSEP from random-matrix theory
• Symmetry resolved out-of-time-order correlators of Heisenberg spin chains using projected matrix product operators
• Leading and beyond leading-order spectral form factor in chaotic quantum many-body systems across all Dyson symmetry classes
• Tri-unitary quantum circuits
• Entanglement structure for finite system under dual-unitary dynamics
• Eigenstate Thermalization Hypothesis and Random Matrix Theory Universality in Few-Body Systems
• Statistics-encoded tensor network approach in disordered quantum many-body spin chains
• Solvable random matrix ensemble with a logarithmic weakly confining potential
• Rationally independent free fermions with local hopping
• Weak-Memory Dynamics in Discrete Time
• Random quantum circuits, chaos and quantum thermalization
• Non-Equilibrium Quantum Many-Body Physics with Quantum Circuits
• Vanishing correlations in stochastic and bistochastic controlled circuits