A closer look at symmetry breaking in the collinear phase of the $J_1-J_2$ Heisenberg Model

TL;DR

This paper investigates the symmetry breaking in the collinear phase of the $J_1-J_2$ Heisenberg model, using theoretical methods to analyze excitation spectra and phase transitions, concluding that the Ising-like transition occurs only at zero temperature.

Contribution

The study combines series expansion and mean-field spin-wave theory to analyze excitation spectra and challenges previous claims of finite temperature symmetry breaking.

Findings

Spectra reveal symmetries of the ordered phase.

No evidence of finite temperature phase transition.

Ising-like transition occurs only at zero temperature.

Abstract

The large $J_2$ limit of the square-lattice $J_1-J_2$ Heisenberg antiferromagnet is a classic example of order by disorder where quantum fluctuations select a collinear ground state. Here, we use series expansion methods and a meanfield spin-wave theory to study the excitation spectra in this phase and look for a finite temperature Ising-like transition, corresponding to a broken symmetry of the square-lattice, as first proposed by Chandra et al. (Phys. Rev. Lett. 64, 88 (1990)). We find that the spectra reveal the symmetries of the ordered phase. However, we do not find any evidence for a finite temperature phase transition. Based on an effective field theory we argue that the Ising-like transition occurs only at zero temperature.