String-charge duality in integrable lattice models

Abstract

We derive an explicit mapping between the spectra of conserved local operators of integrable quantum lattice models and the density distributions of their thermodynamic particle content. This is presented explicitly for the Heisenberg XXZ spin chain. As an application we discuss a quantum quench scenario, in both the gapped and critical regimes. We outline an exact technique which allows for an efficient implementation on periodic matrix product states. In addition, for certain simple product states we obtain analytic closed-form expressions in terms of solutions to Hirota functional relations. Remarkably, no reference to a maximal entropy principle is invoked.

18 pages + appendices, revised version as accepted by JSTAT

References in corpus (24)

• Thermalization and its mechanism for generic isolated quantum systems
• Quantum Quench in the Transverse Field Ising Chain
• Experimental Observation of a Generalized Gibbs Ensemble
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Complete Generalized Gibbs Ensemble in an interacting Theory
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Generalized Thermalization in an Integrable Lattice System
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• "Light-cone" dynamics after quantum quenches in spin chains
• Validity of the GGE for quantum quenches from interacting to noninteracting models
• Generalized Gibbs Ensembles for Quantum Field Theories
• Quasilocal conserved operators in isotropic Heisenberg spin 1/2 chain
• A Shortcut to the Q-Operator
• Quantum quench in the sine-Gordon model
• Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics
• Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
• Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
• Exactly conserved quasilocal operators for the XXZ spin chain
• Quantum quench within the gapless phase of the spin-1/2 Heisenberg XXZ spin-chain
• The Quantum Deformed Mirror TBA I
• Relaxation dynamics of local observables in integrable systems
• Short distance correlators in the XXZ spin chain for arbitrary string distributions
• Quasilocal conservation laws from semicyclic irreducible representations of $U_q({\mathfrak{sl}}_2)$ in $XXZ$ spin-$1/2$ chains
• Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field

Cited by in corpus (91)

• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Entanglement and thermodynamics after a quantum quench in integrable systems
• Finite-temperature transport in one-dimensional quantum lattice models
• Hydrodynamic Diffusion in Integrable Systems
• Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
• Bethe-Boltzmann Hydrodynamics and Spin Transport in the XXZ Chain
• Entanglement dynamics after quantum quenches in generic integrable systems
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• Microscopic origin of ideal conductivity in integrable quantum models
• Roadmap on Atomtronics: State of the art and perspective
• Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach
• Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
• Analytic solution of the Domain Wall non-equilibrium stationary state
• Super-diffusion in one-dimensional quantum lattice models
• Non-equilibrium spin transport in integrable spin chains: persistent currents and emergence of magnetic domains
• Generalized hydrodynamics with space-time inhomogeneous interactions
• Superdiffusion in spin chains
• The isolated Heisenberg magnet as a quantum time crystal
• From Interacting Particles to Equilibrium Statistical Ensembles
• Determination of the Nonequilibrium Steady State Emerging from a Defect
• Entanglement and quantum transport in integrable systems
• Quench action and Renyi entropies in integrable systems
• Superuniversality of superdiffusion
• Exact steady states for quantum quenches in integrable Heisenberg spin chains
• Thermalization and light cones in a model with weak integrability breaking
• Thermalization and pseudolocality in extended quantum systems
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Full Counting Statistics in the Transverse Field Ising Chain
• Entanglement spreading in non-equilibrium integrable systems
• Correlations and diagonal entropy after quantum quenches in XXZ chains
• Quantum quenches to the attractive one-dimensional Bose gas: exact results
• Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
• Energy transport in an integrable parafermionic chain via generalized hydrodynamics
• Front dynamics and entanglement in the XXZ chain with a gradient
• Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws
• How order melts after quantum quenches
• Integrability-protected adiabatic reversibility in quantum spin chains
• Breakdown of Tan's relation in lossy one-dimensional Bose gases
• Towards a Generalized Hydrodynamics description of Rényi entropies in integrable systems
• Spreading of entanglement and correlations after a quench with intertwined quasiparticles
• Generalized Deep Thermalization for Free Fermions
• Integrable Matrix Product States from boundary integrability
• Approximate light cone effects in a non-relativistic quantum field theory after a local quench
• Low-Temperature Transport in Out-of-Equilibrium XXZ Chains
• Anomalous transport from hot quasiparticles in interacting spin chains
• Excited state correlations of the finite Heisenberg chain
• Hydrodynamics of nonintegrable systems from a relaxation-time approximation
• Integrable Matrix Models in Discrete Space-Time
• Quasi-local charges and the Generalized Gibbs Ensemble in the Lieb-Liniger model
• Quantum Quench in a Harmonically Trapped One-Dimensional Bose Gas
• Generalized Hydrodynamics of the attractive Non-Linear Schroedinger Equation
• Exact Thermodynamics and Transport in the Classical Sine-Gordon Model
• Exact out-of-equilibrium steady states in the semiclassical limit of the interacting Bose gas
• Diffusive Hydrodynamics of Inhomogenous Hamiltonians
• Probing non-thermal density fluctuations in the one-dimensional Bose gas
• Adiabatic formation of bound states in the 1d Bose gas
• Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices
• Real-Time Evolution in the Hubbard Model with Infinite Repulsion
• Transport through interacting defects and lack of thermalisation
• Engineering generalized Gibbs ensembles with trapped ions
• Quenches from gaussian bosons to Tonks-Girardeau gas: stationary states and effects of a confining potential
• Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics
• Superluminal moving defects in the Ising spin chain
• Perturbative post-quench overlaps in Quantum Field Theory
• Dissipation-driven integrable fermionic systems: from graded Yangians to exact nonequilibrium steady states
• Superdiffusion from nonabelian symmetries in nearly integrable systems
• Integrability breaking in the one dimensional Bose gas: Atomic losses and energy loss
• Systematic strong coupling expansion for out-of-equilibrium dynamics in the Lieb-Liniger model
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• Hydrodynamics of massless integrable RG flows and a non-equilibrium c-theorem
• Popcorn Drude weights from quantum symmetry
• Parametrically long lifetime of superdiffusion in non-integrable spin chains
• The equilibrium landscape of the Heisenberg spin chain
• Iterative construction of conserved quantities in dissipative nearly integrable systems
• Strong Eigenstate Thermalization within a Generalized Shell in Noninteracting Integrable Systems
• Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects
• Strongly correlated non-equilibrium steady states with currents --- quantum and classical picture
• Generalized Gibbs Ensemble and string-charge relations in nested Bethe Ansatz
• Convergence radius of perturbative Lindblad driven non-equilibrium steady states
• Disorder-Order Interface Propagating over the Ferromagnetic Ground State in the Transverse Field Ising Chain
• Experimental Investigation of a Bipartite Quench in a 1D Bose gas
• Anomalous charge transport in the sine-Gordon model
• Ballistic conductance with and without disorder in a boundary-driven XXZ spin chain
• Observation of a generalized Gibbs ensemble in photonics
• Probes of Full Eigenstate Thermalization in Ergodicity-Breaking Quantum Circuits
• Integrable Floquet QFT: Elasticity and factorization under periodic driving
• Full counting statistics after quantum quenches as hydrodynamic fluctuations
• On the Q operator and the spectrum of the XXZ model at root of unity
• Bound-state confinement after trap-expansion dynamics in integrable systems
• Exotic critical states as fractional Fermi seas in the one-dimensional Bose gas
• Time evolution of effective central charge and signatures of RG irreversibility after a quantum quench