Short distance correlators in the XXZ spin chain for arbitrary string distributions

Abstract

In this letter we consider expectation values of local correlators in highly excited states of the spin-1/2 XXZ chain. Assuming that the string hypothesis holds we formulate the following conjecture: The correlation functions can be computed using the known factorized formulas of the finite temperature situation, if the building blocks are computed via certain linear integral equations using the string densities only. We prove this statement for the nearest neighbour z-z correlator for states with arbitrary string densities. Also, we check the conjecture numerically for other correlators in the finite temperature case. Our results pave the way towards the computation of the stationary values of correlators in non-equilibrium situations using the so-called quench-action approach.

15 pages, v2: minor modifications, v3: minor modifications

References in corpus (5)

• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain
• Mean values of local operators in highly excited Bethe states
• Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field
• On the algebraic Bethe Ansatz approach to the correlation functions of the XXZ spin-1/2 Heisenberg chain

Cited by in corpus (10)

• Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
• Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
• Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain
• Correlations and diagonal entropy after quantum quenches in XXZ chains
• Failure of the Generalized Eigenstate Thermalization Hypothesis in integrable models with multiple particle species
• Exact solution for the quench dynamics of a nested integrable system
• Quantum quenches and Generalized Gibbs Ensemble in a Bethe Ansatz solvable lattice model of interacting bosons
• Local correlations in the attractive 1D Bose gas: from Bethe ansatz to the Gross-Pitaevskii equation
• General finite-size effects for zero-entropy states in one-dimensional quantum integrable models
• Generalized Gibbs Ensemble and string-charge relations in nested Bethe Ansatz