Quantum phase transitions: The mean-field perspective

TL;DR

This paper presents a mean-field approach to analyze quantum phase transitions in a $J-J'$ quantum Heisenberg antiferromagnet, using a variational ansatz to describe the transition driven by the ratio of exchange couplings.

Contribution

It introduces a simple mean-field-like variational method to study quantum phase transitions in quantum spin models, aligning with Landau theory.

Findings

Ground-state energy and order parameter calculated

Quantum phase transition described within the Landau framework

Method generalizable to more complex quantum spin models

Abstract

To illustrate a simple mean-field-like approach for examining quantum phase transitions we consider the $J-J^\prime$ quantum Heisenberg antiferromagnet on a square lattice. The exchange couplings $J$ and $J^\prime$ are competing with each other. The ratio $J^\prime/J$ is the control parameter and its change drives the transition. We adopt a variational ansatz, calculate the ground-state energy as well as the order parameter and describe the quantum phase transition inherent in the model. This description corresponds completely to the standard Landau theory of phase transitions. We also discuss how to generalize such an approach for more complicated quantum spin models.