Multi-point correlation functions in the boundary XXZ chain at finite temperature

TL;DR

This paper develops a method to express multi-point correlation functions in the open XXZ chain at finite temperature using quantum transfer matrix sums, incorporating boundary effects explicitly, and provides explicit formulas for boundary spin correlations.

Contribution

It introduces a novel form factor expansion framework for open boundary integrable models at finite temperature, explicitly including boundary field effects.

Findings

Correlation functions expressed as sums over thermal form factors

Explicit formulas for boundary spin one-point functions

Solves longstanding problem of form factor expansions with open boundaries

Abstract

We consider multi-point correlation functions in the open XXZ chain with longitudinal boundary fields and in a uniform external magnetic field. We show that, at finite temperature, these correlation functions can be written in the quantum transfer matrix framework as sums over thermal form factors. More precisely, and quite remarkably, each term of the sum is given by a simple product of usual matrix elements of the quantum transfer matrix multiplied by a unique factor containing the whole information about the boundary fields. As an example, we provide a detailed expression for the longitudinal spin one-point functions at distance $m$ from the boundary. This work thus solves the long-standing problem of setting up form factor expansions in integrable models subject to open boundary conditions.