Continuous similarity transformation for critical phenomena: easy-axis antiferromagnetic XXZ model

TL;DR

This paper uses continuous similarity transformations to analyze the easy-axis antiferromagnetic XXZ model, providing a detailed understanding of its ground state, excitations, and critical behavior across different anisotropies.

Contribution

The study introduces a truncated CST approach to derive an effective Hamiltonian for the XXZ model, enabling quantitative analysis of excitations and critical phenomena.

Findings

Quantitative ground-state energy and magnon dispersion results.

Identification of the gap closing and critical behavior.

Analysis of two-magnon bound states and their decay.

Abstract

We apply continuous similarity transformations (CSTs) to the easy-axis antiferromagnetic XXZ-model on the square lattice. The CST flow equations are truncated in momentum space by the scaling dimension $d$ so that all contributions with $d\le 2$ are taken into account. The resulting quartic magnon-conserving effective Hamiltonian is analyzed in the zero-, one-, and two-magnon sector. In this way, a quantitative description of the ground-state energy, the one-magnon dispersion and its gap as well as of two-magnon bound states is gained for anisotropies ranging from the gapped Ising model to the gapless Heisenberg model. We discuss the critical properties of the gap closing as well as the evolution of the one-magnon roton mininum. The excitation energies of two-magnon bound states are calculated and their decay into the two-magnon continuum is determined via the inverse participation ratio.