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

TL;DR

This paper proposes a method to compute local correlators in highly excited states of the XXZ spin chain using known finite temperature formulas and string densities, with proofs and numerical checks supporting the conjecture.

Contribution

It formulates and proves a conjecture relating correlators in excited states to finite temperature formulas via string densities, advancing non-equilibrium analysis.

Findings

Proved the conjecture for the nearest neighbor z-z correlator.

Numerically verified the conjecture for other correlators at finite temperature.

Established a framework for computing stationary correlators in non-equilibrium states.

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.