Correlation functions of the open XXZ chain II

TL;DR

This paper derives compact formulas for spin correlation functions in the semi-infinite XXZ chain with boundary magnetic field, revealing boundary-induced oscillations and decay behaviors in physical quantities.

Contribution

It provides new integral formulas for correlation functions and analyzes boundary effects in the XXZ chain, extending previous work with effective re-summations.

Findings

Local magnetization exhibits Friedel oscillations near the boundary.

Energy density profiles decay algebraically with distance from the boundary.

Boundary magnetic field influences oscillation amplitudes.

Abstract

We derive compact multiple integral formulas for several physical spin correlation functions in the semi-infinite XXZ chain with a longitudinal boundary magnetic field. Our formulas follow from several effective re-summations of the multiple integral representation for the elementary blocks obtained in our previous article (I). In the free fermion point we compute the local magnetization as well as the density of energy profiles. These quantities, in addition to their bulk behavior, exhibit Friedel type oscillations induced by the boundary; their amplitudes depend on the boundary magnetic field and decay algebraically in terms of the distance to the boundary.