Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos

Abstract

The most general and versatile defining feature of quantum chaotic systems is that they possess an energy spectrum with correlations universally described by random matrix theory (RMT). This feature can be exhibited by systems with a well defined classical limit as well as by systems with no classical correspondence, such as locally interacting spins or fermions. Despite great phenomenological success, a general mechanism explaining the emergence of RMT without reference to semiclassical concepts is still missing. Here we provide the example of a quantum many-body system with no semiclassical limit (no large parameter) where the emergence of RMT spectral correlations is proven exactly. Specifically, we consider a periodically driven Ising model and write the Fourier transform of spectral density's two-point function, the spectral form factor, in terms of a partition function of a two-dimensional classical Ising model featuring a space-time duality. We show that the self-dual cases provide a minimal model of many-body quantum chaos, where the spectral form factor is demonstrated to match RMT for all values of the integer time variable $t$ in the thermodynamic limit. In particular, we rigorously prove RMT form factor for odd $t$, while we formulate a precise conjecture for even $t$. The results imply ergodicity for any finite amount of disorder in the longitudinal field, rigorously excluding the possibility of many-body localization. Our method provides a novel route for obtaining exact nonperturbative results in non-integrable systems.

arXiv comment6 + 22 pages, 3 figures; v2: improved presentation of the proofs in the appendices; v3: as appears in Physical Review Letters

References in corpus (29)

• Many body localization and thermalization in quantum statistical mechanics
• A bound on chaos
• Operator Spreading in Random Unitary Circuits
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Many-body localization in periodically driven systems
• Semiclassical Foundation of Universality in Quantum Chaos
• Solution of a minimal model for many-body quantum chaos
• Equilibration and Order in Quantum Floquet Matter
• Localization and the effects of symmetries in the thermalization properties of one-dimensional quantum systems
• Spectral statistics in spatially extended chaotic quantum many-body systems
• Periodic-Orbit Theory of Universality in Quantum Chaos
• Matrix Product States for dynamical simulation of infinite chains
• On general relation between quantum ergodicity and fidelity of quantum dynamics
• Many-body quantum chaos: Analytic connection to random matrix theory
• Onset of Random Matrix Behavior in Scrambling Systems
• The spectral form factor is not self-averaging
• Ergodic properties of a generic non-integrable quantum many-body system in thermodynamic limit
• Leading off-diagonal approximation for the spectral form factor for uniformly hyperbolic systems
• 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
• Statistical properties of the spectrum the extended Bose-Hubbard model
• Chaos and Complexity of quantum motion
• Coherent Backscattering in Fock Space: a Signature of Quantum Many-Body Interference in Interacting Bosonic Systems
• Universal Quantum Graphs
• Spectral statistics of chaotic many-body systems
• Semiclassical Identification of Periodic Orbits in a Quantum Many-Body System
• Periodic Mean-Field Solutions and the Spectra of Discrete Bosonic Fields: Trace Formula for Bose-Hubbard Models
• Semiclassical Theory for Universality in Quantum Chaos with Symmetry Crossover

Cited by in corpus (252)

• Measurement-driven entanglement transition in hybrid quantum circuits
• Random Quantum Circuits
• Quantum chaos challenges many-body localization
• A Universal Operator Growth Hypothesis
• A Race Track Trapped-Ion Quantum Processor
• Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
• Exact dynamics in dual-unitary quantum circuits
• A semiclassical ramp in SYK and in gravity
• Postselection-free entanglement dynamics via spacetime duality
• Entanglement spreading in a minimal model of maximal many-body quantum chaos
• Unitary circuits of finite depth and infinite width from quantum channels
• Spectral statistics and many-body quantum chaos with conserved charge
• Adiabatic eigenstate deformations as a sensitive probe for quantum chaos
• The entanglement membrane in chaotic many-body systems
• Ergodic and non-ergodic dual-unitary quantum circuits with arbitrary local Hilbert space dimension
• Many-Body Localization in the Age of Classical Computing
• Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality
• Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits
• Scrambling in Random Unitary Circuits: Exact Results
• Exact thermalization dynamics in the "Rule 54" Quantum Cellular Automaton
• Spacetime duality between localization transitions and measurement-induced transitions
• Exact emergent quantum state designs from quantum chaotic dynamics
• 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
• Digital Quantum Simulation, Trotter Errors, and Quantum Chaos of the Kicked Top
• Euclidean operator growth and quantum chaos
• 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
• Dynamical purification and the emergence of quantum state designs from the projected ensemble
• From dual-unitary to quantum Bernoulli circuits: Role of the entangling power in constructing a quantum ergodic hierarchy
• Probing many-body quantum chaos with quantum simulators
• An exponential ramp in the quadratic Sachdev-Ye-Kitaev model
• A Random Unitary Circuit Model for Black Hole Evaporation
• Many-body level statistics of single-particle quantum chaos
• Spectral statistics in constrained many-body quantum chaotic systems
• Temporal entanglement, quasiparticles and the role of interactions
• Thermofield dynamics: Quantum Chaos versus Decoherence
• Kardar-Parisi-Zhang physics in integrable rotationally symmetric dynamics on discrete space-time lattice
• Entanglement dynamics in hybrid quantum circuits
• Dynamics and Transport at the Threshold of Many-Body Localization
• Random Matrix Spectral Form Factor of Dual-Unitary Quantum Circuits
• Operator Entanglement in Local Quantum Circuits II: Solitons in Chains of Qubits
• Solvable model of deep thermalization with distinct design times
• Many-body delocalisation as symmetry breaking
• Scrambling is Necessary but Not Sufficient for Chaos
• Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
• Subdiffusion and many-body quantum chaos with kinetic constraints
• Model of level statistics for disordered interacting quantum many-body systems
• Localization with random time-periodic quantum circuits
• Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
• Magic spreading in random quantum circuits
• 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
• Holographic dynamics simulations with a trapped ion quantum computer
• Universal spectral form factor for many-body localization
• Apparent slow dynamics in the ergodic phase of a driven many-body localized system without extensive conserved quantities
• Entanglement Negativity and Mutual Information after a Quantum Quench: Exact Link from Space-Time Duality
• Stability of many-body localization in Floquet systems
• Entanglement in many-body eigenstates of quantum-chaotic quadratic Hamiltonians
• Dynamical signatures of quantum chaos and relaxation timescales in a spin-boson system
• Bounds in Nonequilibrium Quantum Dynamics
• Maximal entanglement velocity implies dual unitarity
• Random Matrix Spectral Form Factor in Kicked Interacting Fermionic Chains
• Chaos and Ergodicity in Extended Quantum Systems with Noisy Driving
• Coherence requirements for quantum communication from hybrid circuit dynamics
• Spectral Lyapunov exponents in chaotic and localized many-body quantum systems
• Dynamics of charge fluctuations from asymmetric initial states
• Construction and the ergodicity properties of dual unitary quantum circuits
• Correlations and commuting transfer matrices in integrable unitary circuits
• Exact local correlations in kicked chains at light cone edges
• Exceptional Dynamical Quantum Phase Transitions in Periodically Driven Systems
• Temporal Entanglement in Chaotic Quantum Circuits
• Many-body quantum chaos and emergence of Ginibre ensemble
• Monitoring Quantum Simulators via Quantum Non-Demolition Couplings to Atomic Clock Qubits
• Scaling of temporal entanglement in proximity to integrability
• Semiclassical roots of universality in many-body quantum chaos
• Transition from Quantum Chaos to Localization in Spin Chains
• Operator Spreading in Quantum Maps
• Statistics of the Spectral Form Factor in the Self-Dual Kicked Ising Model
• Exact dynamics in dual-unitary quantum circuits with projective measurements
• Regularization dependence of the OTOC. Which Lyapunov spectrum is the physical one?
• Self-averaging in many-body quantum systems out of equilibrium: Chaotic systems
• Many Body Quantum Chaos and Dual Unitarity Round-a-Face
• Many-body quantum chaos in stroboscopically-driven cold atoms
• Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality
• Transport and entanglement growth in long-range random Clifford circuits
• Measurement-induced phases of matter require feedback
• Measuring Spectral Form Factor in Many-Body Chaotic and Localized Phases of Quantum Processors
• A Yang-Baxter integrable cellular automaton with a four site update rule
• Signatures of Chaos in Non-integrable Models of Quantum Field Theory
• Many-Body Quantum Chaos and Space-time Translational Invariance
• Non-equilibrium dynamics of charged dual-unitary circuits
• Growth of entanglement of generic states under dual-unitary dynamics
• Spectral decoupling in many-body quantum chaos
• Shadow tomography from emergent state designs in analog quantum simulators
• From integrability to chaos in quantum Liouvillians
• Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains
• From Dual Unitarity to Generic Quantum Operator Spreading
• Construction and local equivalence of dual-unitary operators: from dynamical maps to quantum combinatorial designs
• Dynamical quantum ergodicity from energy level statistics
• Hierarchical generalization of dual unitarity
• Full Eigenstate Thermalization via Free Cumulants in Quantum Lattice Systems
• Crystalline Quantum Circuits
• Note on entropy dynamics in the Brownian SYK model
• Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg chain
• Entanglement transitions as a probe of quasiparticles and quantum thermalization
• Statistics of phase space localization measures and quantum chaos in the kicked top model
• Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits
• Weak integrability breaking and level spacing distribution
• 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
• Dual unitary circuits in random geometries
• Non-equilibrium dynamics of symmetry-resolved entanglement and entanglement asymmetry: Exact asymptotics in Rule 54
• Circuits of space and time quantum channels
• Exact solution of long-range stabilizer Rényi entropy in the dual-unitary XXZ model
• Exact Spectral Statistics in Strongly Localised Circuits
• Ternary unitary quantum lattice models and circuits in $2+1$ dimensions
• Krylov complexity and Trotter transitions in unitary circuit dynamics
• Quantum information spreading in generalised dual-unitary circuits
• Thermalisation Dynamics and Spectral Statistics of Extended Systems with Thermalising Boundaries
• Quantum Many-Body Scars in Dual-Unitary Circuits
• Emergence of many-body quantum chaos via spontaneous breaking of unitarity
• Multifractality in quasienergy space of coherent states as a signature of quantum chaos
• Operator Growth from Global Out-of-time-order Correlators
• Robustness of quantum chaos and anomalous relaxation in open quantum circuits
• Quantifying quantum chaos through microcanonical distributions of entanglement
• Renormalization group for measurement and entanglement phase transitions
• Real-time correlators in chaotic quantum many-body systems
• Random-matrix behavior of quantum nonintegrable many-body systems with Dyson's three symmetries
• Entanglement entropy growth in stochastic conformal field theory and the KPZ class
• The entanglement membrane in exactly solvable lattice models
• Macroscopic effects of localised measurements in jammed states of quantum spin chains
• The operator growth hypothesis in open quantum systems
• Universal Dephasing Mechanism of Many-Body Quantum Chaos
• Fock-space delocalization and the emergence of the Porter-Thomas distribution from dual-unitary dynamics
• Signatures of information scrambling in the dynamics of the entanglement spectrum
• From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics
• Spectral statistics of a minimal quantum glass model
• Signatures of quantum chaos in low-energy mixtures of few fermions
• Zero-temperature entanglement membranes in quantum circuits
• Spectral form factors of clean and random quantum Ising chains
• Dynamical simulations of many-body quantum chaos on a quantum computer
• Exact universal bounds on quantum dynamics and fast scrambling
• A universal bound on Quantum Chaos from Random Matrix Theory
• Dynamics of spectral correlations in the entanglement Hamiltonian of the Aubry-André-Harper model
• Quantum Chaos in the Extended Dicke Model
• Operator dynamics in Floquet many-body systems
• Exactly solvable many-body dynamics from space-time duality
• Exact pre-transition effects in kinetically constrained circuits: dynamical fluctuations in the Floquet-East model
• Dynamics and Phases of Nonunitary Floquet Transverse-Field Ising Model
• Coarse-grained Entanglement and Operator Growth in Anomalous Dynamics
• Operator dynamics and entanglement in space-time dual Hadamard lattices
• Spread complexity and quantum chaos for periodically driven spin chains
• Towards Quantum Gravity in the Lab on Quantum Processors
• Mixing and localisation in random time-periodic quantum circuits of Clifford unitaries
• Quantum simulation using noisy unitary circuits and measurements
• Universal Properties of the Spectral Form Factor in Open Quantum Systems
• Absence of localization in two-dimensional Clifford circuits
• Universal late-time dynamics in isolated one-dimensional statistical systems with topological excitations
• Integrable spin chains and cellular automata with medium range interaction
• Quantum and Classical Dynamics with Random Permutation Circuits
• Solvable entanglement dynamics in quantum circuits with generalized space-time duality
• Exact Hidden Markovian Dynamics in Quantum Circuits
• Classical route to ergodicity and scarring in collective quantum systems
• Scalable simulation of non-equilibrium quantum dynamics via classically optimised unitary circuits
• Space-Time Duality between Quantum Chaos and Non-Hermitian Boundary Effect
• Free Independence and the Noncrossing Partition Lattice in Dual-Unitary Quantum Circuits
• Operator Space Entangling Power of Quantum Dynamics and Local Operator Entanglement Growth in Dual-Unitary Circuits
• Diagnosing Quantum Many-body Chaos in Non-Hermitian Quantum Spin Chain via Krylov Complexity
• Symmetry breaking in chaotic many-body quantum systems at finite temperature
• Analyticity constraints bound the decay of the spectral form factor
• Loschmidt echo, emerging dual unitarity and scaling of generalized temporal entropies after quenches to the critical point
• Local correlations in dual-unitary kicked chains
• Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor
• Single-Particle Universality of the Many-Body Spectral Form Factor
• Localization and integrability breaking in weakly interacting Floquet circuits
• Dual unitaries as maximizers of the distance to local product gates
• Fundamental charges for dual-unitary circuits
• Quantum circuits with free fermions in disguise
• Many-body quantum chaos in mixtures of multiple species
• Nonlocality of Deep Thermalization
• Construction of perfect tensors using biunimodular vectors
• Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics
• Exact results on the dynamics of the stochastic Floquet-East model
• Hopf algebras and solvable unitary circuits
• Measurement-induced entanglement and complexity in random constant-depth 2D quantum circuits
• Streamlined Krylov construction and classification of ergodic Floquet systems
• Integrability breaking and bound states in Google's decorated XXZ circuits
• Exact spectral form factors of non-interacting fermions with Dyson statistics
• Universal distributions of overlaps from generic dynamics in quantum many-body systems
• Fisher zeroes and the fluctuations of the spectral form factor of chaotic systems
• Random matrix universality in dynamical correlation functions at late times
• Out-of-Time-Order-Correlator for van der Waals potential
• Effective field theory of random quantum circuits
• Simulating Floquet scrambling circuits on trapped-ion quantum computers
• Long-ranged spectral correlations in eigenstate phases
• Entanglement in dual unitary quantum circuits with impurities
• Structural Stability Hypothesis of Dual Unitary Quantum Chaos
• Spectral form factors and dynamical localization
• Spectral Form Factors of Topological Phases
• Solvable Quantum Circuits in Tree+1 Dimensions
• Hilbert subspace ergodicity
• Universal correlations in chaotic many-body quantum states: Fock-space formulation of Berrys random wave model
• Hilbert space average of transition probabilities
• Late-time ensembles of quantum states in quantum chaotic systems
• Protecting Quantum Information via Many-Body Dynamical Localization
• No-resonance conditions, random matrices, and quantum chaotic models
• Entanglement patterns of quantum chaotic Hamiltonians with a scalar U(1) charge
• Localization in the Kicked Ising Chain
• Deviations from random matrix entanglement statistics for kicked quantum chaotic spin-$1/2$ chains
• Critical quantum dynamics of observables at eigenstate transitions
• Scrambling in Ising spin systems with periodic transverse magnetic fields
• Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling
• Statistics of local level spacings in single- and many-body quantum chaos
• Hierarchical analytical approach to universal spectral correlations in Brownian Quantum Chaos
• Geometric constructions of generalized dual-unitary circuits from biunitarity
• Transition to chaos in extended systems and their quantum impurity models
• Statistics of the Random Matrix Spectral Form Factor
• Walsh-Floquet Theory of Periodic Kick Drives
• Growth of Rényi Entropies in Interacting Integrable Models and the Breakdown of the Quasiparticle Picture
• SYK model based $\beta$ regime dependent two-qubit dynamical wormhole-inspired teleportation protocol simulation
• Spectral Statistics of Non-Hermitian Matrices and Dissipative Quantum Chaos
• Signatures of quantum chaos and complexity in the Ising model on random graphs
• Hierarchy of timescales in a disordered spin-$1/2$ XX ladder
• Dynamics of Loschmidt echoes from operator growth in noisy quantum many-body systems
• Spectral anomalies and broken symmetries in maximally chaotic quantum maps
• Field theory of charge sharpening in symmetric monitored quantum circuits
• Detecting few-body quantum chaos: out-of-time ordered correlators at saturation
• Superintegrable cellular automata and dual unitary gates from Yang-Baxter maps
• Edge of Many-Body Quantum Chaos in Quantum Reservoir Computing
• Stringent Test on Power Spectrum of Quantum Integrable and Chaotic Systems
• Boundary Chaos: Spectral Form Factor
• Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics
• Discrete time crystals detected by time-translation twist
• Tri-unitary quantum circuits
• Leading and beyond leading-order spectral form factor in chaotic quantum many-body systems across all Dyson symmetry classes
• Thouless Energy Across Many-Body Localization Transition in Floquet Systems
• From eigenstate thermalization to hydrodynamic transport in correlated metals
• Noisy Monitored Quantum Circuits
• Engineering entanglement geometry via spacetime-modulated measurements
• Rationally independent free fermions with local hopping
• Eigenstate Thermalization Hypothesis and Random Matrix Theory Universality in Few-Body Systems
• Statistics-encoded tensor network approach in disordered quantum many-body spin chains
• Quantum Complexity in Rule-Based Constrained Many-Body Models: Scars, Fragmentation, and Chaos
• Floquet thermalization by power-law induced permutation symmetry breaking
• Finding periodic orbits in projected quantum many-body dynamics
• Crystalline Spectral Form Factors
• Non-Equilibrium Quantum Many-Body Physics with Quantum Circuits
• Vanishing correlations in stochastic and bistochastic controlled circuits
• Limitations of SVD-Based Diagnostics for Non-Hermitian Many-Body Localization with Time-Reversal Symmetry