The LeClair-Mussardo series and nested Bethe Ansatz

Abstract

We consider correlation functions in one dimensional quantum integrable models related to the algebra symmetries $\mathfrak{gl}(2|1)$ and $\mathfrak{gl}(3)$. Using the algebraic Bethe Ansatz approach we develop an expansion theorem, which leads to an infinite integral series in the thermodynamic limit. The series is the generalization of the LeClair-Mussardo series to nested Bethe Ansatz systems, and it is applicable both to one-point and two-point functions. As an example we consider the ground state density-density correlator in the Gaudin-Yang model of spin-1/2 Fermi particles. Explicit formulas are presented in a special large coupling and large imbalance limit.

arXiv comment39 pages, v2: minor changes

References in corpus (49)

• 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
• Quantum Inverse Scattering Method and Correlation Functions
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Complete Generalized Gibbs Ensemble in an interacting Theory
• Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field
• On the quantum inverse scattering problem
• Integral representations for correlation functions of the XXZ chain at finite temperature
• Spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field
• Finite Temperature Correlation Functions in Integrable QFT
• Form factors in finite volume II:disconnected terms and finite temperature correlators
• Asymptotic factorisation of form factors in two-dimensional quantum field theory
• Form factor approach to dynamical correlation functions in critical models
• Master equation for spin-spin correlation functions of the XXZ chain
• Solution of the quantum inverse problem
• Exact large-scale correlations in integrable systems out of equilibrium
• 1D Lieb-Liniger Bose Gas as Non-Relativistic Limit of the Sinh-Gordon Model
• Expectation Values in the Lieb-Liniger Bose Gas
• A comment on finite temperature correlations in integrable QFT
• Form factor approach to the asymptotic behavior of correlation functions in critical models
• Dynamical correlation functions of the XXZ spin-1/2 chain
• Mean values of local operators in highly excited Bethe states
• Local correlations in the 1D Bose gas from a scaling limit of the XXZ chain
• Short distance correlators in the XXZ spin chain for arbitrary string distributions
• Thermal form-factor approach to dynamical correlation functions of integrable lattice models
• On correlation functions of integrable models associated to the six-vertex R-matrix
• Form factors in quantum integrable models with GL(3)-invariant R-matrix
• Current operators in integrable spin chains: lessons from long range deformations
• Thermal form factors of the XXZ chain and the large-distance asymptotics of its temperature dependent correlation functions
• Finite temperature correlation functions from form factors
• Form factors in SU(3)-invariant integrable models
• Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas
• Low-temperature large-distance asymptotics of the transversal two-point functions of the XXZ chain
• Scalar products in generalized models with SU(3)-symmetry
• A note on the spin-1/2 XXZ chain concerning its relation to the Bose gas
• Sine-Gordon form factors in finite volume
• Scalar products of Bethe vectors in models with $\mathfrak{gl}(2|1)$ symmetry 2. Determinant representation
• On Form Factors in nested Bethe Ansatz systems
• On form-factor expansions for the XXZ chain in the massive regime
• Diagonal Form Factors and Heavy-Heavy-Light Three-Point Functions at Weak Coupling
• Multiple Actions of the Monodromy Matrix in $\mathfrak{gl}(2|1)$-Invariant Integrable Models
• Higher conservation laws for the quantum non-linear Schroedinger equation
• Thermal form factor approach to the ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime
• Low-temperature spectrum of correlation lengths of the XXZ chain in the antiferromagnetic massive regime
• Correlation functions of the integrable $SU(n)$ spin chain
• On the calculation of the correlation functions of the ${\mathfrak{sl}}_3$-model by means of the reduced qKZ equation
• Correlation functions of integrable $O(n)$ spin chains
• Asymptotic behaviour of two-point functions in multi-species models
• On the finite volume expectation values of local operators in the sine-Gordon model

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• Current operators in integrable models: A review
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