Zero temperature phase transitions in quantum Heisenberg ferromagnets

TL;DR

This paper investigates zero temperature phase transitions in quantum Heisenberg ferromagnets, introducing new lattice models of quantum rotors, analyzing their phase diagrams, and exploring universality classes across different dimensions.

Contribution

It introduces a new class of quantum rotor lattice models and analyzes their phase diagrams and low-energy behaviors, linking them to fermionic systems.

Findings

Phase transitions in 1D itinerant Fermi systems match rotor model universality.

Mean-field phase diagrams of the new models are computed.

Implications for higher-dimensional fermionic systems are discussed.

Abstract

The purpose of this work is to understand the zero temperature phases, and the phase transitions, of Heisenberg spin systems which can have an extensive, spontaneous magnetic moment; this entails a study of quantum transitions with an order parameter which is also a non-abelian conserved charge. To this end, we introduce and study a new class of lattice models of quantum rotors. We compute their mean-field phase diagrams, and present continuum, quantum field-theoretic descriptions of their low energy properties in different regimes. We argue that, in spatial dimension $d=1$, the phase transitions in itinerant Fermi systems are in the same universality class as the corresponding transitions in certain rotor models. We discuss implications of our results for itinerant fermions systems in higher $d$, and for other physical systems.