Spin-1/2 XXZ Heisenberg chain in a longitudinal magnetic field

TL;DR

This paper applies a tensor renormalization method to the XXZ Heisenberg model in a magnetic field, accurately capturing its ground state, spectrum, and phase structure while maintaining symmetry and efficiency.

Contribution

It introduces a tensor renormalization approach that preserves U(1) symmetry, enabling efficient and accurate analysis of the XXZ model's properties.

Findings

Accurately reproduces phase structure from fixed point tensors

Achieves high accuracy with moderate computational effort

Successfully compares results with Bethe Ansatz calculations

Abstract

We study the XXZ Heisenberg model in a longitudinal magnetic field using a tensor renormalization method. Built into the tensor representation of the XXZ model is the U(1) symmetry, which is systematically maintained at each renormalization step. This enables rather large tensor representations. We extract ground state properties as well as the low lying spectrum from the fixed point tensors. With rather moderate numerical effort we achieve a very good accuracy as demonstrated by comparison with Bethe Ansatz calculations. The phase structure of the model can be accurately reproduced just from the largest fixed point tensor elements.