Particle-Time Duality in the Kicked Ising Chain I: The Dual Operator

Abstract

We demonstrate that the dynamics of kicked spin chains possess a remarkable duality property. The trace of the unitary evolution operator for $N$ spins at time $T$ is related to one of a non-unitary evolution operator for $T$ spins at time $N$. We investigate the spectrum of this dual operator with a focus on the different parameter regimes (chaotic, regular) of the spin chain. We present applications of this duality relation to spectral statistics in an accompanying paper.

14 pages, 5 figures

References in corpus (11)

• Semiclassical Foundation of Universality in Quantum Chaos
• Matrix Product States for dynamical simulation of infinite chains
• Periodic-Orbit Theory of Level Correlations
• Chaos and Complexity of quantum motion
• Connecting Entanglement in Time and Space: Improving the Folding Algorithm
• Spectral statistics of chaotic many-body systems
• Non-universal level statistics in a chaotic quantum spin chain
• Classical foundations of many-particle quantum chaos
• The spectral form factor near the Ehrenfest-time
• Semiclassical excited-state signatures of quantum phase transitions in spin chains with variable-range interactions
• Two dimensional kicked quantum Ising model: dynamical phase transitions

Cited by in corpus (93)

• Random Quantum Circuits
• Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
• A Race Track Trapped-Ion Quantum Processor
• Exact dynamics in dual-unitary quantum circuits
• Entanglement spreading in a minimal model of maximal many-body quantum chaos
• Many-body quantum chaos: Analytic connection to random matrix theory
• The entanglement membrane in chaotic many-body systems
• Many-Body Localization in the Age of Classical Computing
• Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality
• Operator entanglement entropy of the time evolution operator in chaotic systems
• Spacetime duality between localization transitions and measurement-induced transitions
• Exact emergent quantum state designs from quantum chaotic dynamics
• 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
• Solvable model of deep thermalization with distinct design times
• Many-body delocalisation as symmetry breaking
• Scrambling is Necessary but Not Sufficient for Chaos
• 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
• Holographic dynamics simulations with a trapped ion quantum computer
• Entanglement Negativity and Mutual Information after a Quantum Quench: Exact Link from Space-Time Duality
• Stability of many-body localization in Floquet systems
• Spectral Lyapunov exponents in chaotic and localized many-body quantum systems
• Semiclassical Identification of Periodic Orbits in a Quantum Many-Body System
• Exact local correlations in kicked chains at light cone edges
• Exceptional Dynamical Quantum Phase Transitions in Periodically Driven Systems
• Many-body quantum chaos and emergence of Ginibre ensemble
• 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
• Statistics of the Spectral Form Factor in the Self-Dual Kicked Ising Model
• Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality
• Many Body Quantum Chaos and Dual Unitarity Round-a-Face
• Many-Body Quantum Chaos and Space-time Translational Invariance
• From Dual Unitarity to Generic Quantum Operator Spreading
• Construction and local equivalence of dual-unitary operators: from dynamical maps to quantum combinatorial designs
• Entanglement measures of bipartite quantum gates and their thermalization under arbitrary interaction strength
• Crystalline Quantum Circuits
• 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
• Quantum Many-Body Scars in Dual-Unitary Circuits
• The entanglement membrane in exactly solvable lattice models
• Renormalization group for measurement and entanglement phase transitions
• Real-time correlators in chaotic quantum many-body systems
• Fock-space delocalization and the emergence of the Porter-Thomas distribution from dual-unitary dynamics
• From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics
• Zero-temperature entanglement membranes in quantum circuits
• Dynamical simulations of many-body quantum chaos on a quantum computer
• Boundary Chaos
• Operator dynamics and entanglement in space-time dual Hadamard lattices
• Exactly solvable many-body dynamics from space-time duality
• Spread complexity and quantum chaos for periodically driven spin chains
• Semiclassical Prediction of Large Spectral Fluctuations in Interacting Kicked Spin Chains
• Space-Time Duality between Quantum Chaos and Non-Hermitian Boundary Effect
• Free Independence and the Noncrossing Partition Lattice in Dual-Unitary Quantum Circuits
• Temporal Entanglement Barriers in Dual-Unitary Clifford Circuits with Measurements
• Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation
• Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor
• Quantum circuits with free fermions in disguise
• Localization and integrability breaking in weakly interacting Floquet circuits
• Dual unitaries as maximizers of the distance to local product gates
• Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics
• Nonlocality of Deep Thermalization
• Streamlined Krylov construction and classification of ergodic Floquet systems
• Construction of perfect tensors using biunimodular vectors
• Bulk-boundary correspondence from hyper-invariant tensor networks
• Characterizing quantum chaoticity of kicked spin chains
• Persistent Ballistic Entanglement Spreading with Optimal Control in Quantum Spin Chains
• Classification of same-gate quantum circuits and their space-time symmetries with application to the level-spacing distribution
• Structural Stability Hypothesis of Dual Unitary Quantum Chaos
• Hilbert space average of transition probabilities
• Solvable Quantum Circuits in Tree+1 Dimensions
• Geometric constructions of generalized dual-unitary circuits from biunitarity
• Walsh-Floquet Theory of Periodic Kick Drives
• Localization in the Kicked Ising Chain
• Influence functional of many-body systems: temporal entanglement and matrix-product state representation
• Deviations from random matrix entanglement statistics for kicked quantum chaotic spin-$1/2$ chains
• Kicked-Ising Quantum Battery
• Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics
• Boundary Chaos: Spectral Form Factor
• Discrete time crystals detected by time-translation twist
• Collectivity and Periodic Orbits in a Chain of Interacting, Kicked Spins
• Floquet thermalization by power-law induced permutation symmetry breaking
• Out-of-time-order correlation and detection of phase structure in Floquet transverse Ising spin system
• 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
• Tri-unitary quantum circuits
• Finding periodic orbits in projected quantum many-body dynamics