The Quench Action

Abstract

We give a pedagogical introduction to the methodology of the Quench Action, which is an effective representation for the calculation of time-dependent expectation values of physical operators following a generic out-of-equilibrium state preparation protocol (for example a quantum quench). The representation, originally introduced in [Caux and Essler, Phys. Rev. Lett. 110, 257203 (2013)], is founded on a mixture of exact data for overlaps together with variational reasonings. It is argued to be quite generally valid and thermodynamically exact for arbitrary times after the quench (from short times all the way up to the steady state), and applicable to a wide class of physically relevant observables. Here, we introduce the method and its language, give an overview of some recent results, suggest a roadmap and offer some perspectives on possible future research directions.

Article for the JSTAT special issue: Quantum Integrability in Out of Equilibrium Systems

References in corpus (49)

• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Quantum Quench in the Transverse Field Ising Chain
• Generalized Gibbs ensemble in integrable lattice models
• Experimental Observation of a Generalized Gibbs Ensemble
• Breakdown of thermalization in finite one-dimensional systems
• The Luttinger model following a sudden interaction switch-on
• Quantum quenches in 1+1 dimensional conformal field theories
• 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
• Spin-Orbital Separation in the quasi 1D Mott-insulator Sr2CuO3
• Quasilocal charges in integrable lattice systems
• Quantum quench dynamics of the Luttinger model
• Prethermalization and universal dynamics in near-integrable quantum systems
• Nonequilibrium quantum dynamics and transport: from integrability to many-body localization
• Conformal field theory out of equilibrium: a review
• Validity of the GGE for quantum quenches from interacting to noninteracting models
• Generalized Gibbs Ensembles for Quantum Field Theories
• Quantum quench in the sine-Gordon model
• Quantum quench dynamics of the sine-Gordon model in some solvable limits
• Dynamical structure factor of one-dimensional Bose gases: experimental signatures of beyond-Luttinger liquid physics
• Generalized TBA and generalized Gibbs
• Dynamics in the Ising field theory after a quantum quench
• Direct Observation of Magnon Fractionalization in the Quantum Spin Ladder
• Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
• Quantum quenches from integrability: the fermionic pairing model
• Relaxation dynamics in the gapped XXZ spin-1/2 chain
• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions
• Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain
• Stationary states in a free fermionic chain from the Quench Action Method
• Quantum quenches in the sinh-Gordon model: steady state and one point correlation functions
• Equilibration Properties of Classical Integrable Field Theories
• Multimode dynamics and emergence of a characteristic length-scale in a one-dimensional quantum system
• Quantum Quenches in the Luttinger model and its close relatives
• Pre-relaxation in weakly interacting models
• Failure of the Generalized Eigenstate Thermalization Hypothesis in integrable models with multiple particle species
• Short distance correlators in the XXZ spin chain for arbitrary string distributions
• Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons
• One-point functions in massive integrable QFT with boundaries
• Interaction quench in a trapped one-dimensional Bose gas
• Quantum quench in long-range field theories
• Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis
• Density form factors of the 1D Bose gas for finite entropy states
• Form factors of integrable Heisenberg (higher) spin chains
• Thermalization away from Integrability and the Role of Operator Off-Diagonal Elements
• Towards a Non-equilibrium Bethe ansatz for the Kondo Model
• Interaction quenches in the Lieb-Liniger model

Cited by in corpus (170)

• Generalized Gibbs ensemble in integrable lattice models
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Thermalization and prethermalization in isolated quantum systems: a theoretical overview
• Entanglement and thermodynamics after a quantum quench in integrable systems
• Quantum quenches in 1+1 dimensional conformal field theories
• Quasilocal charges in integrable lattice systems
• Entanglement dynamics after quantum quenches in generic integrable systems
• Prethermalization and universal dynamics in near-integrable quantum systems
• Nonequilibrium quantum dynamics and transport: from integrability to many-body localization
• Exact dynamics in dual-unitary quantum circuits
• Roadmap on Atomtronics: State of the art and perspective
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Entanglement and matrix elements of observables in interacting integrable systems
• Prethermalization and Thermalization in Isolated Quantum Systems
• Non-equilibrium spin transport in integrable spin chains: persistent currents and emergence of magnetic domains
• Generalized hydrodynamics with space-time inhomogeneous interactions
• Eigenstate Thermalization in a Locally Perturbed Integrable System
• Signatures of rare states and thermalization in a theory with confinement
• Exact thermalization dynamics in the "Rule 54" Quantum Cellular Automaton
• Correlation functions and transport coefficients in generalised hydrodynamics
• From Interacting Particles to Equilibrium Statistical Ensembles
• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Generalized Hydrodynamics in the 1D Bose gas: theory and experiments
• Entanglement and quantum transport in integrable systems
• Spreading of correlations in Markovian open quantum systems
• Quench action and Renyi entropies in integrable systems
• Extension of the Generalized Hydrodynamics to the Dimensional Crossover Regime
• Exact steady states for quantum quenches in integrable Heisenberg spin chains
• Thermalization and light cones in a model with weak integrability breaking
• Entanglement evolution and generalised hydrodynamics: interacting integrable systems
• Universality in the onset of quantum chaos in many-body systems
• Time-dependent generalized Gibbs ensembles in open quantum systems
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Quantum information scrambling after a quantum quench
• Transport in the sine-Gordon field theory: from generalized hydrodynamics to semiclassics
• Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain
• Temporal entanglement, quasiparticles and the role of interactions
• Entanglement spreading in non-equilibrium integrable systems
• Correlations and diagonal entropy after quantum quenches in XXZ chains
• Equilibration Properties of Classical Integrable Field Theories
• Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
• Pumping approximately integrable systems
• Quantum quenches to the attractive one-dimensional Bose gas: exact results
• Integrability of $1D$ Lindbladians from operator-space fragmentation
• Rényi entropies after releasing the Néel state in the XXZ spin-chain
• Eigenstate thermalization hypothesis and integrals of motion
• Energy transport in an integrable parafermionic chain via generalized hydrodynamics
• Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54
• Heating Rates in Periodically Driven Strongly Interacting Quantum Many-Body Systems
• Integrability-protected adiabatic reversibility in quantum spin chains
• Spreading of entanglement and correlations after a quench with intertwined quasiparticles
• Towards a Generalized Hydrodynamics description of Rényi entropies in integrable systems
• From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics
• Absence of Normal Fluctuations in an Integrable Magnet
• Exact dynamics following an interaction quench in a one-dimensional anyonic gas
• Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains
• Generalized Deep Thermalization for Free Fermions
• Dynamics of charge fluctuations from asymmetric initial states
• Integrable Matrix Product States from boundary integrability
• Entangled multiplets and unusual spreading of quantum correlations in a continuously monitored tight-binding chain
• Dissipative quasi-particle picture for quadratic Markovian open quantum systems
• Approximate light cone effects in a non-relativistic quantum field theory after a local quench
• Quasi locality of the GGE in interacting-to-free quenches in relativistic field theories
• Exact correlations in the Lieb-Liniger model and detailed balance out-of-equilibrium
• Fragmentation and emergent integrable transport in the weakly tilted Ising chain
• Generalized hydrodynamics: a perspective
• Emergent local integrals of motion without a complete set of localized eigenstates
• Quasi-local charges and the Generalized Gibbs Ensemble in the Lieb-Liniger model
• Thermodynamic bootstrap program for integrable QFT's: Form factors and correlation functions at finite energy density
• Quantum Quench in a Harmonically Trapped One-Dimensional Bose Gas
• Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion
• Measuring effective temperatures in a generalized Gibbs ensemble
• Quench action and large deviations: work statistics in the one-dimensional Bose gas
• Generalized Hydrodynamics of the attractive Non-Linear Schroedinger Equation
• A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model
• Prethermalization from a low-density Holstein-Primakoff expansion
• Exact Thermodynamics and Transport in the Classical Sine-Gordon Model
• Universal short-time dynamics: boundary functional renormalization group for a temperature quench
• Euler-scale dynamical correlations in integrable systems with fluid motion
• Inner products in integrable Richardson-Gaudin models
• Logarithmic negativity in out-of-equilibrium open free-fermion chains: An exactly solvable case
• Exact out-of-equilibrium steady states in the semiclassical limit of the interacting Bose gas
• Adiabatic formation of bound states in the 1d Bose gas
• Crosscap States in Integrable Field Theories and Spin Chains
• Simulating the out-of-equilibrium dynamics of local observables by trading entanglement for mixture
• Non-equilibrium dynamics of symmetry-resolved entanglement and entanglement asymmetry: Exact asymptotics in Rule 54
• Time-dependent Correlation Functions in Open Quadratic Fermionic Systems
• Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices
• Can the Macroscopic Fluctuation Theory be Quantized?
• Quenches in initially coupled Tomonaga-Luttinger Liquids: a conformal field theory approach
• Real-Time Evolution in the Hubbard Model with Infinite Repulsion
• Integrable quenches in the Hubbard model
• Numerical linked cluster expansions for quantum quenches in one dimensional lattices
• Solution of the BEC to BCS Quench in One Dimension
• Engineering generalized Gibbs ensembles with trapped ions
• Large time and long distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas
• How generalized hydrodynamics time evolution arises from a form factor expansion
• Entanglement entropy in a periodically driven quantum Ising chain
• Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics
• Effective free-fermionic form factors and the XY spin chain
• Loschmidt Echo of Far-From-Equilibrium Fermionic Superfluids
• Systematic strong coupling expansion for out-of-equilibrium dynamics in the Lieb-Liniger model
• Exact large-scale fluctuations of the phase field in the sine-Gordon model
• Non-Equilibrium Quantum Spin Dynamics from Classical Stochastic Processes
• Full Counting Statistics of Charge in Quenched Quantum Gases
• Experimental observation of repulsively bound magnons
• On the Dynamics of Free-Fermionic Tau-Functions at Finite Temperature
• Closed hierarchy of Heisenberg equations in integrable models with Onsager algebra
• Non-equilibrium aspects of integrable models
• Quantum quench dynamics of the attractive one-dimensional Bose gas via the coordinate Bethe ansatz
• Interplay of Solitons and Radiation in One-Dimensional Bose Gases
• Dynamics of nonlinear-Schroedinger breathers in a potential trap
• The Floquet Baxterisation
• Transport and entanglement across integrable impurities from Generalized Hydrodynamics
• Integrable Quantum Circuits from the Star-Triangle Relation
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• Inelastic decay from integrability
• The equilibrium landscape of the Heisenberg spin chain
• Dynamical fermionization in a one-dimensional Bose-Fermi mixture
• The two particle-hole pairs contribution to the dynamic correlation functions of quantum integrable models
• Quantum Work of an Optical Lattice
• Power-law decay of correlations after a global quench in the massive XXZ chain
• Iterative construction of conserved quantities in dissipative nearly integrable systems
• Quantum adiabatic protocols using emergent local Hamiltonians
• Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects
• Work extraction in an isolated quantum lattice system: Grand canonical and generalized Gibbs ensemble predictions
• Nonequilibrium symmetry-protected topological order: emergence of semilocal Gibbs ensembles
• Navier-Stokes equations for nearly integrable quantum gases
• Low-density limit of dynamical correlations in the Lieb-Liniger model
• One-Loop Non-Planar Anomalous Dimensions in Super Yang-Mills Theory
• Exact Overlaps in the Lieb-Liniger Model from Coordinate Bethe Ansatz
• Mobile impurity in a one-dimensional gas at finite temperatures
• Quantum Thermalization and the Expansion of Atomic Clouds
• Integrable Crosscap States: From Spin Chains to 1D Bose Gas
• Continuum approach to real time dynamics of 1+1D gauge field theory: out of horizon correlations of the Schwinger model
• Mixed-order symmetry-breaking quantum phase transition far from equilibrium
• The relevant excitations for the one-body function in the Lieb-Liniger model
• Connected correlations in partitioning protocols: a case study and beyond
• Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain
• Probing chaos in the spherical p-spin glass model
• Generalized hydrodynamics of integrable quantum circuits
• Relaxation dynamics of integrable field theories after a global quantum quench
• Dynamical fermionization in one-dimensional spinor gases at finite temperature
• Determinant formula for the field form factor in the anyonic Lieb-Liniger model
• Quantum quench in a driven Ising chain
• Integrability of Goldilocks quantum cellular automata
• Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations
• General interaction quenches in a Luttinger liquid
• The Theory of Generalised Hydrodynamics for the One-dimensional Bose Gas
• New equilibrium ensembles for isolated quantum systems
• Thermalization/Relaxation in integrable and free field theories: an Operator Thermalization Hypothesis
• Non-Equilibrium Steady State of the Lieb-Liniger model: exact treatment of the Tonks Girardeau limit
• Quasicondensation and off-diagonal long-range order of hard-core bosons during a free expansion
• Chapman-Enskog theory and crossover between diffusion and superdiffusion for nearly integrable quantum gases
• Nonequilibrium dynamics in one-dimensional strongly interacting two-component gases
• Growth of Rényi Entropies in Interacting Integrable Models and the Breakdown of the Quasiparticle Picture
• Quantum quenches in the sinh-Gordon and Lieb-Liniger models
• Quantum quench and thermalization to GGE in arbitrary dimensions and the odd-even effect
• Full counting statistics after quantum quenches as hydrodynamic fluctuations
• On computing non-equilibrium dynamics following a quench
• Spectrum-preserving deformations of integrable spin chains with open boundaries
• Entanglement of Stationary States in the Presence of Unstable Quasiparticles
• On the Q operator and the spectrum of the XXZ model at root of unity
• Extending the Thermodynamic Form Factor Bootstrap Program: Multiple particle-hole excitations, crossing symmetry, and reparameterization invariance
• Thermodynamics of classical integrable field theories
• Local Properties of the Rapidity Distribution in the Lieb-Liniger Model
• Expansion of one-dimensional spinor gases from power-law traps
• Exotic critical states as fractional Fermi seas in the one-dimensional Bose gas
• Temperature and conditions for thermalization after canonical quenches
• Theoretical study on thermalization in isolated quantum systems