Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions

Abstract

We consider a class of quantum lattice models in $1+1$ dimensions represented as local quantum circuits that enjoy a particular "dual-unitarity" property. In essence, this property ensures that both the evolution "in time" and that "in space" are given in terms of unitary transfer matrices. We show that for this class of circuits, generically non-integrable, one can compute explicitly all dynamical correlations of local observables. Our result is exact, non-pertubative, and holds for any dimension $d$ of the local Hilbert space. In the minimal case of qubits ($d=2$) we also present a classification of all dual-unitary circuits which allows us to single out a number of distinct classes for the behaviour of the dynamical correlations. We find "non-interacting" classes, where all correlations are preserved, the ergodic and mixing one, where all correlations decay, and, interestingly, also classes that are are both interacting and non-ergodic.

arXiv comment6+5 pages, no figures; v2 minor changes; v3 as appears in Phys. Rev. Lett

References in corpus (20)

• Many-Body Physics with Ultracold Gases
• Quantum Inverse Scattering Method and Correlation Functions
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Optimal Quantum Circuits for General Two-Qubit Gates
• Optimal Creation of Entanglement Using a Two--Qubit Gate
• Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
• Solution of a minimal model for many-body quantum chaos
• Entanglement spreading in a minimal model of maximal many-body quantum chaos
• On general relation between quantum ergodicity and fidelity of quantum dynamics
• Unitary circuits of finite depth and infinite width from quantum channels
• Sub-ballistic growth of Rényi entropies due to diffusion
• Integrable Trotterization: Local Conservation Laws and Boundary Driving
• Ballistic spin transport in a periodically driven integrable quantum system
• Ergodic properties of a generic non-integrable quantum many-body system in thermodynamic limit
• Integrable Floquet dynamics
• Chaos and Complexity of quantum motion
• Unitary quantum gates, perfect entanglers and unistochastic maps
• Ergodic Properties of Infinite Harmonic Crystals: an Analytic Approach
• Ergodic Properties of the Quantum Ideal Gas in the Maxwell-Boltzmann Statistics

Cited by in corpus (207)

• Random Quantum Circuits
• A Race Track Trapped-Ion Quantum Processor
• Information Scrambling in Computationally Complex Quantum Circuits
• Exact dynamics in dual-unitary quantum circuits
• Postselection-free entanglement dynamics via spacetime duality
• Operator scaling dimensions and multifractality at measurement-induced transitions
• 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
• Maximum velocity quantum circuits
• Influence matrix approach to many-body Floquet dynamics
• Local pairing of Feynman histories in many-body Floquet models
• Information Scrambling over Bipartitions: Equilibration, Entropy Production, and Typicality
• 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
• Creating ensembles of dual unitary and maximally entangling quantum evolutions
• Temporal entanglement, quasiparticles and the role of interactions
• Entanglement dynamics in hybrid quantum circuits
• Kardar-Parisi-Zhang physics in integrable rotationally symmetric dynamics on discrete space-time lattice
• Operator Entanglement in Local Quantum Circuits II: Solitons in Chains of Qubits
• Many-body delocalisation as symmetry breaking
• Random Matrix Spectral Form Factor of Dual-Unitary Quantum Circuits
• Solvable model of deep thermalization with distinct design times
• Scrambling is Necessary but Not Sufficient for Chaos
• Entanglement dynamics in Rule 54: Exact results and quasiparticle picture
• Computational power of one- and two-dimensional dual-unitary quantum circuits
• Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
• Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
• Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions
• Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
• Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54
• Time evolution of correlation functions in quantum many-body systems
• Thirty-six entangled officers of Euler: Quantum solution to a classically impossible problem
• Entanglement Barriers in Dual-Unitary Circuits
• Holographic dynamics simulations with a trapped ion quantum computer
• Entanglement Negativity and Mutual Information after a Quantum Quench: Exact Link from Space-Time Duality
• Maximal entanglement velocity implies dual unitarity
• Chaos and Ergodicity in Extended Quantum Systems with Noisy Driving
• Generalized Deep Thermalization for Free Fermions
• Simulating hydrodynamics on noisy intermediate-scale quantum devices with random circuits
• Construction and the ergodicity properties of dual unitary quantum circuits
• Dynamics of charge fluctuations from asymmetric initial states
• Correlations and commuting transfer matrices in integrable unitary circuits
• Exact local correlations in kicked chains at light cone edges
• Many-body quantum chaos and emergence of Ginibre ensemble
• Temporal Entanglement in Chaotic Quantum Circuits
• Exceptional Dynamical Quantum Phase Transitions in Periodically Driven Systems
• Scaling of temporal entanglement in proximity to integrability
• Semiclassical roots of universality in many-body quantum chaos
• Statistics of the Spectral Form Factor in the Self-Dual Kicked Ising Model
• Exact dynamics in dual-unitary quantum circuits with projective measurements
• Integrable Matrix Models in Discrete Space-Time
• Many Body Quantum Chaos and Dual Unitarity Round-a-Face
• Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality
• Transport and entanglement growth in long-range random Clifford circuits
• A Yang-Baxter integrable cellular automaton with a four site update rule
• Non-equilibrium dynamics of charged dual-unitary circuits
• Growth of entanglement of generic states under dual-unitary dynamics
• Shadow tomography from emergent state designs in analog quantum simulators
• Exact solution of the Floquet-PXP cellular automaton
• 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
• Dynamical quantum ergodicity from energy level statistics
• Hierarchical generalization of dual unitarity
• Crystalline Quantum Circuits
• Full Eigenstate Thermalization via Free Cumulants in Quantum Lattice Systems
• Topological lower bound on quantum chaos by entanglement growth
• Prethermalisation and Thermalisation in the Entanglement Dynamics
• Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits
• Spectral form factor in a minimal bosonic model of many-body quantum chaos
• Two-step phantom relaxation of out-of-time-ordered correlations in random circuits
• Circuits of space and time quantum channels
• Non-equilibrium dynamics of symmetry-resolved entanglement and entanglement asymmetry: Exact asymptotics in Rule 54
• Dual unitary circuits in random geometries
• Exact quench dynamics of the Floquet quantum East model at the deterministic point
• Exact solution of long-range stabilizer Rényi entropy in the dual-unitary XXZ model
• Exact Spectral Statistics in Strongly Localised Circuits
• Magic Resources of the Heisenberg Picture
• Ternary unitary quantum lattice models and circuits in $2+1$ dimensions
• Space-like dynamics in a reversible cellular automaton
• Quantum information spreading in generalised dual-unitary circuits
• Krylov complexity and Trotter transitions in unitary circuit dynamics
• Thermalisation Dynamics and Spectral Statistics of Extended Systems with Thermalising Boundaries
• Operator front broadening in chaotic and integrable quantum chains
• Quantum Many-Body Scars in Dual-Unitary Circuits
• Absolutely maximally entangled state equivalence and the construction of infinite quantum solutions to the problem of 36 officers of Euler
• Momentum dependent quantum Ruelle-Pollicott resonances in translationally invariant many-body systems
• Boundary transfer matrix spectrum of measurement-induced transitions
• Robustness of quantum chaos and anomalous relaxation in open quantum circuits
• Three-fold way of entanglement dynamics in monitored quantum circuits
• Fock-space delocalization and the emergence of the Porter-Thomas distribution from dual-unitary dynamics
• The entanglement membrane in exactly solvable lattice models
• Real-time correlators in chaotic quantum many-body systems
• From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics
• Floquet integrability and long-range entanglement generation in the one-dimensional quantum Potts model
• Zero-temperature entanglement membranes in quantum circuits
• Dynamical simulations of many-body quantum chaos on a quantum computer
• Exact universal bounds on quantum dynamics and fast scrambling
• Integrable deformations of superintegrable quantum circuits
• Integrable nonunitary quantum circuits
• An integrable spin chain with Hilbert space fragmentation and solvable real time dynamics
• Operator dynamics in Floquet many-body systems
• Exactly solvable many-body dynamics from space-time duality
• Operator dynamics and entanglement in space-time dual Hadamard lattices
• Dynamics and Phases of Nonunitary Floquet Transverse-Field Ising Model
• Exact pre-transition effects in kinetically constrained circuits: dynamical fluctuations in the Floquet-East model
• Boundary Chaos: Exact Entanglement Dynamics
• Boundary Chaos
• Quantum simulation using noisy unitary circuits and measurements
• Diagonal unitary and orthogonal symmetries in quantum theory II: Evolution operators
• Entanglement distillation toward minimal bond cut surface in tensor networks
• Quantum and Classical Dynamics with Random Permutation Circuits
• Fisher zeros and persistent temporal oscillations in non-unitary quantum circuits
• Quench dynamics in lattices above one dimension: the free fermionic case
• Universal late-time dynamics in isolated one-dimensional statistical systems with topological excitations
• Absence of localization in two-dimensional Clifford circuits
• Space-Time Duality between Quantum Chaos and Non-Hermitian Boundary Effect
• Two-step relaxation in local many-body Floquet systems
• Exact solution of the Rule 150 reversible cellular automaton
• Exact Hidden Markovian Dynamics in Quantum Circuits
• Loschmidt echo, emerging dual unitarity and scaling of generalized temporal entropies after quenches to the critical point
• Free Independence and the Noncrossing Partition Lattice in Dual-Unitary Quantum Circuits
• Temporal Entanglement Barriers in Dual-Unitary Clifford Circuits with Measurements
• Local correlations in dual-unitary kicked chains
• Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor
• Tensor network decompositions for absolutely maximally entangled states
• Operator Space Entangling Power of Quantum Dynamics and Local Operator Entanglement Growth in Dual-Unitary Circuits
• Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation
• Localization and integrability breaking in weakly interacting Floquet circuits
• Dual unitaries as maximizers of the distance to local product gates
• Capturing long-range memory structures with tree-geometry process tensors
• Fundamental charges for dual-unitary circuits
• The spatiotemporal doubled density operator: a unified framework for analyzing spatial and temporal quantum processes
• Exact results on the dynamics of the stochastic Floquet-East model
• Hopf algebras and solvable unitary circuits
• Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems
• Construction of perfect tensors using biunimodular vectors
• Many-body quantum chaos in mixtures of multiple species
• Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics
• Critical Properties of Weak Measurement Induced Phase Transitions in Random Quantum Circuits
• Dual-isometric Projected Entangled Pair States
• Quantum complexity phase transitions in monitored random circuits
• Streamlined Krylov construction and classification of ergodic Floquet systems
• Exact Correlation Functions for Dual-Unitary Quantum circuits with exceptional points
• Measurement-induced entanglement and complexity in random constant-depth 2D quantum circuits
• Integrability of Goldilocks quantum cellular automata
• Bulk-boundary correspondence from hyper-invariant tensor networks
• Information Flow in Non-Unitary Quantum Cellular Automata
• Dynamics of operator size distribution in q-local quantum Brownian SYK and spin models
• Ergodic theory of diagonal orthogonal covariant quantum channels
• Entanglement of Disjoint Intervals in Dual-Unitary Circuits: Exact Results
• Effective field theory of random quantum circuits
• Classification of same-gate quantum circuits and their space-time symmetries with application to the level-spacing distribution
• Integrability and charge transport in asymmetric quantum-circuit geometries
• Efficient post-selection in light-cone correlations of monitored quantum circuits
• Lanczos-Pascal approach to correlation functions in chaotic quantum systems
• Entanglement in dual unitary quantum circuits with impurities
• Entangling power, gate typicality, and measurement-induced phase transitions
• Structural Stability Hypothesis of Dual Unitary Quantum Chaos
• Noise Induced Universal Diffusive Transport in Fermionic Chains
• Entanglement Propagation in Integrable Heisenberg Chains from a New Lens
• Geometric representations of braid and Yang-Baxter gates
• Hilbert subspace ergodicity
• Solvable Quantum Circuits in Tree+1 Dimensions
• Entanglement dynamics and Page curves in random permutation circuits
• Growth of Rényi Entropies in Interacting Integrable Models and the Breakdown of the Quasiparticle Picture
• Partial projected ensembles and spatiotemporal structure of information scrambling
• Geometric constructions of generalized dual-unitary circuits from biunitarity
• Quantum convolutional channels and multiparameter families of 2-unitary matrices
• Probes of Full Eigenstate Thermalization in Ergodicity-Breaking Quantum Circuits
• Quantum Entanglement Phase Transitions and Computational Complexity: Insights from Ising Models
• Loschmidt echo and scrambling of systematic errors in tomography -- a quantum signature of chaos
• Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits
• Influence functional of many-body systems: temporal entanglement and matrix-product state representation
• Dual-unitary shadow tomography
• Kinetics of information scrambling in correlated electrons: disorder-driven transition from shock-wave to FKPP dynamics
• Localization in the Kicked Ising Chain
• Dynamics of Loschmidt echoes from operator growth in noisy quantum many-body systems
• Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics
• Boundary Chaos: Spectral Form Factor
• Field theory of charge sharpening in symmetric monitored quantum circuits
• Quantum Circuits for High-Dimensional Absolutely Maximally Entangled States
• Superintegrable cellular automata and dual unitary gates from Yang-Baxter maps
• More global randomness from less-random local gates
• Tri-unitary quantum circuits
• Anomalous transport in U(1)-symmetric quantum circuits
• Leading and beyond leading-order spectral form factor in chaotic quantum many-body systems across all Dyson symmetry classes
• Entanglement transition and suppression of critical phase of thermofield double state in monitored quantum circuit with unitary $R$ matrix gates
• Finding periodic orbits in projected quantum many-body dynamics
• Entanglement structure for finite system under dual-unitary dynamics
• Roughening Transition in Quantum Circuits
• Absolutely maximally entangled pure states of multipartite quantum systems
• Process Tensor Approaches to Non-Markovian Quantum Dynamics
• Liouvillian Exceptional Points in Quantum Brickwork Circuits
• Entanglement Growth from Entangled States: A Unified Perspective on Entanglement Generation and Transport
• Noisy Monitored Quantum Circuits
• Measurement-and Feedback-Driven Non-Equilibrium Phase Transitions on a Quantum Processor
• Non-Equilibrium Quantum Many-Body Physics with Quantum Circuits
• Vanishing correlations in stochastic and bistochastic controlled circuits
• Logarithmic growth of operator entanglement in a clean non-integrable circuit
• Random quantum circuits, chaos and quantum thermalization
• Engineering entanglement geometry via spacetime-modulated measurements