# Scaling in the massive antiferromagnetic XXZ spin-1/2 chain near the isotropic point

## TL;DR

This paper investigates the finite-size and temperature scaling behaviors of the antiferromagnetic XXZ spin-1/2 chain near the isotropic point, revealing universal functions that describe energy corrections and free energy dependence.

## Contribution

It provides a numerical calculation of the universal Casimir scaling function for the ground state energy and links it to the temperature dependence of the free energy in the gapped phase.

## Key findings

- Universal Casimir scaling function for ground state energy
- Scaling function describes low-temperature free energy behavior
- Numerical solution of nonlinear integral equation

## Abstract

The scaling limit of the Heisenberg XXZ spin chain at zero magnetic field is studied in the gapped antiferromagnetic phase. For a spin-chain ring having $N_x$ sites, the universal Casimir scaling function, which characterises the leading finite-size correction term in the large-$N_x$ expansion of the ground state energy, is calculated by numerical solution of the nonlinear integral equation of the convolution type. It is shown, that the same scaling function describes the temperature dependence of the free energy of the infinite XXZ chain at low enough temperatures in the gapped scaling regime.