A Semi-Classical Analysis of Order from Disorder

TL;DR

This paper investigates how quantum fluctuations lift classical degeneracy in a Heisenberg antiferromagnet on the Husimi cactus, revealing a semi-classical mechanism that favors specific ground states and influences low-energy excitations.

Contribution

It introduces a semi-classical analysis of order from disorder, distinguishing quantum from thermal effects, and applies it to Kagomé-like lattices to explain ground state selection.

Findings

Quantum fluctuations partially lift classical degeneracy.

Discrete subset of ground states is favored by quantum effects.

Tunneling processes influence low-energy spectrum.

Abstract

We study in this paper the Heisenberg antiferromagnet with nearest neighbours interactions on the Husimi cactus, a system which has locally the same topology as the Kagom\'e lattice. This system has a huge classical degeneracy corresponding to an extensive number of degrees of freedom.We show that unlike thermal fluctuations, quantum fluctuations lift partially this degeneracy and favour a discrete subset of classical ground states. In order to clarify the origin of these effects, we have set up a general semi-classical analysis of the order from disorder phenomenon and clearly identified the differences between classical and quantum fluctuations. This semi-classical approach also enables us to classify various situations where a selection mechanism still occurs. Moreover, once a discrete set of ground states has been preselected, our analysis suggests that tunelling processes within this set should be the dominant effect underlying the strange low energy spectrum of Kagom\'e-like lattices.