Phase diagram of the Heisenberg antiferromagnet with four-spin interactions

TL;DR

This paper maps the phase diagram of a Heisenberg antiferromagnet with four-spin interactions using a hierarchical mean-field approach, revealing a transition from a Néel state to a plaquette-ordered quantum paramagnetic phase.

Contribution

It introduces a single variational ansatz within a hierarchical mean-field framework to comprehensively analyze the phase diagram of the model.

Findings

Identifies a transition between Néel and quantum paramagnetic phases.

Characterizes the non-magnetic phase as a plaquette-ordered state.

Suggests the phase transition aligns with the Landau paradigm.

Abstract

We study the quantum phase diagram of the Heisenberg planar antiferromagnet with a subset of four-spin ring exchange interactions, using the recently proposed heirarchical mean-field approach. By identifying relevant degrees of freedom, we are able to use a single variational anzatz to map the entire phase diagram of the model and uncover the nature of its various phases. It is shown that there exists a transition between a N\'eel state and a quantum paramagnetic phase, characterized by broken translational invariance. The non-magnetic phase preserves the lattice rotational symmetry, and has a correlated plaquette nature. Our results also suggest that this phase transition can be properly described within the Landau paradigm.