Gapped Heisenberg spin chains in a field

TL;DR

This paper studies the anisotropic Heisenberg spin-1/2 chain in a magnetic field, improving mean-field methods with fluctuation corrections, and compares results with numerical and exact solutions.

Contribution

It extends a mean-field approach by including fluctuations and provides quantitative predictions validated against numerical and exact solutions.

Findings

Calculated magnetization, gap, and specific heat agree with numerical data.

Incorporating fluctuations improves the mean-field approximation.

Results match the exact Bethe Ansatz solution at zero field.

Abstract

We consider the fully anisotropic Heisenberg spin-1/2 antiferromagnet in a uniform magnetic field, whose ground-state is characterized by broken spin rotation symmetry and gapped spinon excitations. We expand on a recent mean-field approach to the problem by incorporating fluctuations in a loop expansion. Quantitative results for the magnetization, excitation gap and specific heat are obtained. We compare our predictions with new DMRG and exact diagonalization data and, for zero field, with the exact solution of the ${XYZ}$ spin chain from the Bethe Ansatz.