Luttinger liquid parameters from tensor network data

TL;DR

This paper uses tensor network methods to analyze the XXZ Heisenberg model, extracting Luttinger liquid parameters and phase diagrams, and comparing numerical results with theoretical predictions.

Contribution

It introduces a systematic tensor network approach that preserves U(1) symmetry to determine phase diagrams and scaling dimensions in the XXZ model.

Findings

Accurate phase diagram of the XXZ model obtained.

Scaling dimensions match low-energy field theory predictions.

Tensor network method efficiently captures critical properties.

Abstract

We study the XXZ Heisenberg model in a staggered magnetic field using the HOTRG 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. We determine the phase diagram of the model from the low lying spectrum, and from the finite size dependence of the spectrum we extract scaling dimensions, which are compared to predictions of low energy field theory.