Stability and Absence of a Tower of States in Ferrimagnets

TL;DR

This paper demonstrates that ferrimagnets share key stability and symmetry-breaking features with ferromagnets, lacking a tower of states and exhibiting stable ground states, which challenges previous assumptions about such systems.

Contribution

It analytically and numerically shows that ferrimagnets behave like ferromagnets in symmetry-breaking, lacking a tower of states and having a stable ground state, revealing a generic property of type-B systems.

Findings

Ferrimagnets lack an Anderson tower of states.

The ground state in ferrimagnets is thermodynamically stable.

Properties are shown analytically for Lieb–Mattis ferrimagnet and numerically for Heisenberg ferrimagnet.

Abstract

Antiferromagnets and ferromagnets are archetypes of the two distinct (type-A and type-B) ways of spontaneously breaking a continuous symmetry. Although type-B Nambu--Goldstone modes arise in various systems, the ferromagnet was considered pathological due to the stability and symmetry-breaking nature of its exact ground state. However, here we show that symmetry-breaking in ferrimagnets closely resembles the ferromagnet. In particular, there is an extensive ground state degeneracy, there is no Anderson tower of states, and the maximally polarized ground state is thermodynamically stable. Our results are derived analytically for the Lieb--Mattis ferrimagnet and numerically for the Heisenberg ferrimagnet. We argue that these properties are generic for type-B symmetry-broken systems, where the order parameter operator is a symmetry generator.