Quantum-classical phase transition of the escape rate of two-sublattice antiferromagnetic large spins

TL;DR

This paper investigates the quantum-classical phase transition of the escape rate in a two-sublattice antiferromagnetic spin model, identifying critical coupling values and analyzing phase diagrams using effective potential methods.

Contribution

It introduces a novel analysis of the quantum-classical transition in antiferromagnetic spins with anisotropies, deriving critical coupling conditions and phase diagrams.

Findings

First-order phase transition at J_c=(K+J_z)/2 for the initial model.

Critical coupling J_c=(2K-J_z)/3 for the anisotropic Heisenberg model.

Detailed phase diagrams of the transition are provided.

Abstract

The Hamiltonian of a two-sublattice antiferromagnetic spins, with single (hard-axis) and double ion anisotropies described by $H=J \bold{\hat{S}}_{1}\cdot\bold{\hat{S}}_{2} - 2J_{z}\hat{S}_{1z}\hat{S}_{2z}+K(\hat{S}_{1z}^2 +\hat{S}_{2z}^2)$ is investigated using the method of effective potential. The problem is mapped to a single particle quantum-mechanical Hamiltonian in terms of the relative coordinate and reduced mass. We study the quantum-classical phase transition of the escape rate of this model. We show that the first-order phase transition for this model sets in at the critical value $J_c=\frac{K+J_z}{2}$ while for the anisotropic Heisenberg coupling $H = J(S_{1x}S_{2x} +S_{1y}S_{2y}) + J_zS_{1z}S_{2z} + K(S_{1z}^2+ S_{2z}^2)$ we obtain $J_c=\frac{2K-J_z}{3}$ . The phase diagrams of the transition are also studied.