Overlap singularity and time evolution in integrable quantum field theory

Abstract

We study homogeneous quenches in integrable quantum field theory where the initial state contains zero-momentum particles. We demonstrate that the two-particle pair amplitude necessarily has a singularity at the two-particle threshold. Albeit the explicit discussion is carried out for special (integrable) initial states, we argue that the singularity is inevitably present and is a generic feature of homogeneous quenches involving the creation of zero momentum particles. We also identify the singularity in quenches in the Ising model across the quantum critical point, and compute it perturbatively in phase quenches in the quantum sine-Gordon model which are potentially relevant to experiments. We then construct the explicit time dependence of one-point functions using a linked cluster expansion regulated by a finite volume parameter. We find that the secular contribution normally linear in time is modified by a $t\ln t$ term. We additionally encounter a novel type of secular contribution which is shown to be related to parametric resonance. It is an interesting open question to resum the new contributions and to establish their consequences directly observable in experiments or numerical simulations.

arXiv comment30+45 pages, 7 figures

References in corpus (61)

• 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
• Time-dependence of correlation functions following a quantum quench
• Quantum thermalization through entanglement in an isolated many-body system
• Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
• Relaxation and Pre-thermalization in an Isolated Quantum System
• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Light-cone-like spreading of correlations in a quantum many-body system
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Quantum Quench in the Transverse Field Ising Chain
• Experimental Observation of a Generalized Gibbs Ensemble
• The Luttinger model following a sudden interaction switch-on
• Complete Generalized Gibbs Ensemble in an interacting Theory
• Microscopic observation of magnon bound states and their dynamics
• Local emergence of thermal correlations in an isolated quantum many-body system
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Quasilocal charges in integrable lattice systems
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Quantum quench in an atomic one-dimensional Ising chain
• Quantum Quenches in Integrable Field Theories
• What is an integrable quench?
• Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties
• Dynamical Correlations after a Quantum Quench
• Validity of the GGE for quantum quenches from interacting to noninteracting models
• Analytic results for a quantum quench from free to hard-core one dimensional bosons
• Generalized Gibbs Ensembles for Quantum Field Theories
• Equilibration of a Tonks-Girardeau gas following a trap release
• Form factors in finite volume II:disconnected terms and finite temperature correlators
• Quantum quench in the sine-Gordon model
• Form factors in finite volume I: form factor bootstrap and truncated conformal space
• Quantum Quench from a Thermal Initial State
• Form-factors of exponential fields in the sine-Gordon model
• Semi-classical theory for quantum quenches in finite transverse Ising chains
• Quench dynamics of the interacting Bose gas in one dimension
• Failure of the GGE hypothesis for integrable models with bound states
• Hamiltonian truncation approach to quenches in the Ising field theory
• Form factor expansion for thermal correlators
• An exact formalism for the quench dynamics of integrable models
• Hybrid semiclassical theory of quantum quenches in one dimensional systems
• Quench Dynamics of the Anisotropic Heisenberg Model
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Initial states in integrable quantum field theory quenches from an integral equation hierarchy
• Non-analytic behavior of the Loschmidt echo in XXZ spin chains: exact results
• Boundary State in an Integrable Quantum Field Theory Out of Equilibrium
• Quantum relaxation and finite size effects in the XY chain in a transverse field after global quenches
• Overlaps after quantum quenches in the sine-Gordon model
• Crossover from adiabatic to sudden interaction quench in a Luttinger liquid
• Memory-preserving equilibration after a quantum quench in a 1d critical model
• Relaxation dynamics of local observables in integrable systems
• One-point functions in massive integrable QFT with boundaries
• On the boundary form factor program
• One-point functions in perturbed boundary conformal field theories
• Finite-Size Effects for Multi-Magnon States
• Quantum quench in the attractive regime of the sine-Gordon model
• Finite size effects in quantum field theories with boundary from scattering data
• Semi-classical theory for quantum quenches in the O(3) non-linear sigma model
• Spectral expansion for finite temperature two-point functions and clustering
• Boundary one-point function, Casimir energy and boundary state formalism in D+1 dimensional QFT

Cited by in corpus (23)

• Roadmap on Atomtronics: State of the art and perspective
• Entanglement Oscillations near a Quantum Critical Point
• Entanglement spreading in non-equilibrium integrable systems
• The quantum sine-Gordon model with quantum circuits
• Quench dynamics of the Ising field theory in a magnetic field
• Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions
• Integrable quenches in nested spin chains I: the exact steady states
• Loschmidt Amplitude and Work Distribution in Quenches of the Sine-Gordon Model
• Self-consistent time-dependent harmonic approximation for the sine-Gordon model out of equilibrium
• Josephson oscillations in split one-dimensional Bose gases
• On the low-energy description for tunnel-coupled one-dimensional Bose gases
• Chiral entanglement in massive quantum field theories in 1+1 dimensions
• Perturbative post-quench overlaps in Quantum Field Theory
• Systematic strong coupling expansion for out-of-equilibrium dynamics in the Lieb-Liniger model
• Branch Point Twist Field Form Factors in the sine-Gordon Model I: Breather Fusion and Entanglement Dynamics
• Correlation and entanglement spreading in nested spin chains
• Thermodynamic Bethe Ansatz and Generalised Hydrodynamics in the sine-Gordon model
• On the finite volume expectation values of local operators in the sine-Gordon model
• Relaxation dynamics of integrable field theories after a global quantum quench
• Non-equilibrium time evolution in the sine-Gordon model revisited
• TCSA and the finite volume boundary state
• On computing non-equilibrium dynamics following a quench
• Entanglement of Stationary States in the Presence of Unstable Quasiparticles