Mean values of local operators in highly excited Bethe states

Abstract

We consider expectation values of local operators in (continuum) integrable models in a situation when the mean value is calculated in a single Bethe state with a large number of particles. We develop a form factor expansion for the thermodynamic limit of the mean value, which applies whenever the distribution of Bethe roots is given by smooth density functions. We present three applications of our general result: i) In the framework of integrable Quantum Field Theory (IQFT) we present a derivation of the LeClair-Mussardo formula for finite temperature one-point functions. We also extend the results to boundary operators in Boundary Field Theories. ii) We establish the LeClair-Mussardo formula for the non-relativistic 1D Bose gas in the framework of Algebraic Bethe Ansatz (ABA). This way we obtain an alternative derivation of the results of Kormos et. al. for the (temperature dependent) local correlations using only the concepts of ABA. iii) In IQFT we consider the long-time limit of one-point functions after a certain type of global quench. It is shown that our general results imply the integral series found by Fioretti and Mussardo. We also discuss the generalized Eigenstate Thermalization hypothesis in the context of quantum quenches in integrable models. It is shown that a single mean value always takes the form of a thermodynamic average in a Generalized Gibbs Ensemble, although the relation to the conserved charges is rather indirect.

arXiv comment32 pages, v2: minor changes, v3: minor corrections

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Cited by in corpus (53)

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• Prethermalization and universal dynamics in near-integrable quantum systems
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• What is an integrable quench?
• Relaxation after quantum quenches in the spin-1/2 Heisenberg XXZ chain
• Generalized Gibbs Ensembles for Quantum Field Theories
• Quench Dynamics in a Model with Tuneable Integrability Breaking
• Infinite-time Average of Local Fields in an Integrable Quantum Field Theory after a Quantum Quench
• Correlation functions and transport coefficients in generalised hydrodynamics
• Generalized Hydrodynamics in the 1D Bose gas: theory and experiments
• Thermalization and light cones in a model with weak integrability breaking
• Exact large-scale correlations in integrable systems out of equilibrium
• Exact three-body local correlations for excited states of the 1D Bose gas
• Correlation Functions of the Quantum Sine-Gordon Model in and out of Equilibrium
• Current operators in Bethe Ansatz and Generalized Hydrodynamics: An exact quantum/classical correspondence
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• Exact dynamics following an interaction quench in a one-dimensional anyonic gas
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• Generalized hydrodynamics regime from the thermodynamic bootstrap program
• Quench dynamics of the Ising field theory in a magnetic field
• Approximate light cone effects in a non-relativistic quantum field theory after a local quench
• Quantum quench in long-range field theories
• Form factors and generalized hydrodynamics for integrable systems
• Exact correlations in the Lieb-Liniger model and detailed balance out-of-equilibrium
• Excited state correlations of the finite Heisenberg chain
• Quantum Quench of the trap frequency in the harmonic Calogero model
• 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
• Quench echo and work statistics in integrable quantum field theories
• On Form Factors in nested Bethe Ansatz systems
• Local correlations in the attractive 1D Bose gas: from Bethe ansatz to the Gross-Pitaevskii equation
• Split Fermi seas in one-dimensional Bose fluids
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• LeClair-Mussardo series for two-point functions in Integrable QFT
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• Structure constants of short operators in planar $\mathcal{N}=4$ SYM theory
• Leading exponential finite size corrections for non-diagonal form factors
• Low-density limit of dynamical correlations in the Lieb-Liniger model
• Lattice approach to finite volume form-factors of the Massive Thirring/Sine-Gordon model
• Determinant formula for the field form factor in the anyonic Lieb-Liniger model
• The LeClair-Mussardo series and nested Bethe Ansatz
• Exact mapping from the $(3+1)$-dimensional Skyrme model to the $(1+1)$-dimensional sine-Gordon theory and some applications
• Full counting statistics after quantum quenches as hydrodynamic fluctuations