Boundary susceptibility in the open XXZ-chain

TL;DR

This paper calculates the boundary susceptibility of the open XXZ-chain at zero and finite temperatures using Bethe ansatz, numerical methods, and field theory, providing analytical and numerical insights into boundary effects.

Contribution

It offers the first comprehensive analysis of boundary susceptibility in the open XXZ-chain across various temperature and magnetic field regimes, combining analytical and numerical techniques.

Findings

Analytical expressions for boundary susceptibility at low magnetic fields.

Numerical results for susceptibility profiles near the boundary at finite temperature.

Agreement between Bethe ansatz, numerical DMRG, and bosonization predictions.

Abstract

In the first part we calculate the boundary susceptibility $\chi_B$ in the open $XXZ$-chain at zero temperature and arbitrary magnetic field $h$ by Bethe ansatz. We present analytical results for the leading terms when $|h|\ll \alpha$, where $\alpha$ is a known scale, and a numerical solution for the entire range of fields. In the second part we calculate susceptibility profiles near the boundary at finite temperature $T$ numerically by using the density-matrix renormalization group for transfer matrices and analytically for $T\ll 1$ by field theoretical methods. Finally we compare $\chi_B$ at finite temperature with a low-temperature asymptotics which we obtain by combining our Bethe ansatz result with recent predictions from bosonization.