Rigorous bounds on dynamical response functions and time-translation symmetry breaking
arXiv:2003.01035 · doi:10.21468/SciPostPhys.9.1.003
Abstract
Dynamical response functions are standard tools for probing local physics near the equilibrium. They provide information about relaxation properties after the equilibrium state is weakly perturbed. In this paper we focus on systems which break the assumption of thermalization by exhibiting persistent temporal oscillations. We provide rigorous bounds on the Fourier components of dynamical response functions in terms of extensive or local dynamical symmetries, i.e. extensive or local operators with periodic time dependence. Additionally, we discuss the effects of spatially inhomogeneous dynamical symmetries. The bounds are explicitly implemented on the example of an interacting Floquet system, specifically in the integrable Trotterization of the Heisenberg XXZ model.
arXiv comment18 pages, 3 figures, slightly revised version with new references
References in corpus (38)
- Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
- Observation of discrete time-crystalline order in a disordered dipolar many-body system
- Quantum many-body scars
- Floquet Time Crystals
- Local conservation laws and the structure of the many-body localized states
- On the phase structure of driven quantum systems
- Quantum Time Crystals
- Generalized Gibbs ensemble in integrable lattice models
- Transport and conservation laws
- Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
- Integrals of motion in the Many-Body localized phase
- Time crystals: a review
- Absence of Quantum Time Crystals
- Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
- Emergent SU(2) dynamics and perfect quantum many-body scars
- Non-stationary coherent quantum many-body dynamics through dissipation
- Quasilocal charges in integrable lattice systems
- Periodically Driving a Many-Body Localized Quantum System
- Boundary time crystals
- Absolute Stability and Spatiotemporal Long-Range Order in Floquet systems
- Periodic thermodynamics of isolated systems
- Review: Local Integrals of Motion in Many-Body Localized systems
- Dissipation Induced Structural Instability and Chiral Dynamics in a Quantum Gas
- Discrete time crystals in the absence of manifest symmetries or disorder in open quantum systems
- Quasilocal conserved operators in isotropic Heisenberg spin 1/2 chain
- Dicke time crystals in driven-dissipative quantum many-body systems
- Integrable Trotterization: Local Conservation Laws and Boundary Driving
- Quantum Time Crystals from Hamiltonians with Long-Range Interactions
- Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
- Ballistic spin transport in a periodically driven integrable quantum system
- Systematic construction of scarred many-body dynamics in 1D lattice models
- Thermalization and pseudolocality in extended quantum systems
- Discrete time crystal in globally driven interacting quantum systems without disorder
- Quasilocal conservation laws from semicyclic irreducible representations of in spin- chains
- Topological Time Crystals
- Classical Stochastic Discrete Time Crystals
- Lower bounds on high-temperature diffusion constants from quadratically extensive almost conserved operators
- Auxiliary matrices for the six-vertex model at roots of 1 and a geometric interpretation of its symmetries
Cited by in corpus (29)
- Correlation functions and transport coefficients in generalised hydrodynamics
- Algebraic Theory of Quantum Synchronization and Limit Cycles under Dissipation
- Time Crystals Protected by Floquet Dynamical Symmetry in Hubbard Models
- Lack of symmetry restoration after a quantum quench: an entanglement asymmetry study
- Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
- Unified theory of local quantum many-body dynamics: Eigenoperator thermalization theorems
- Hydrodynamic projections and the emergence of linearised Euler equations in one-dimensional isolated systems
- Signatures of discrete time-crystallinity in transport through an open Fermionic chain
- Out-of-Time-Ordered Crystals and Fragmentation
- Emergence and Dynamical Stability of Charge Time-Crystal in a Current-Carrying Quantum Dot Simulator
- Global Quenches after Localised Perturbations
- Strong zero modes in integrable quantum circuits
- Conjectures on Hidden Onsager Algebra Symmetries in Interacting Quantum Lattice Models
- The Floquet Baxterisation
- Physical ageing from generalised time-translation-invariance
- Quantum many-body spin ratchets
- Long-time dynamics in quantum spin lattices: ergodicity and hydrodynamic projections at all frequencies and wavelengths
- Time-crystalline behavior in central-spin models with Heisenberg interactions
- Noncommuting charges can remove non-stationary quantum many-body dynamics
- Generalized hydrodynamics of integrable quantum circuits
- Integrability of Goldilocks quantum cellular automata
- Opening Krylov space to access all-time dynamics via dynamical symmetries
- Time Crystals from single-molecule magnet arrays
- Protecting coherence from the environment via Stark many-body localization in a Quantum-Dot Simulator
- Fragmentation, Zero Modes, and Collective Bound States in Constrained Models
- Deterministic many-body dynamics with multifractal response
- Stability of emergent time periodicity in a few-body interacting system
- Noninvertible Kramers-Wannier duality symmetries for the discrete-time quantum Ising chain
- Transport in a System with a Tower of Quantum Many-Body Scars