Unveiling Order behind Complexity: Coexistence of Ferromagnetism and Bose-Einstein Condensation

TL;DR

This paper introduces an algebraic framework using SU(N) groups to analyze quantum systems, demonstrating the coexistence of ferromagnetism and Bose-Einstein condensation in a specific spin model.

Contribution

It develops a novel algebraic approach based on local operator dimensions and SU(N) groups, providing exact solutions that reveal coexistence of ferromagnetism and Bose-Einstein condensation.

Findings

Exact solution of the S=1 quantum Heisenberg model at a high symmetry point.

Rigorous proof of coexistence of ferromagnetism and Bose-Einstein condensation.

Framework applicable to quantum systems with local dimension N.

Abstract

We present an algebraic framework for identifying the order parameter and the possible phases of quantum systems that is based on identifying the local dimension $N$ of the quantum operators and using the SU(N) group representing the generators of generalized spin-particle mappings. We illustrate this for $N$=3 by presenting for any spatial dimension the exact solution of the bilinear-biquadratic $S$=1 quantum Heisenberg model at a high symmetry point. Through this solution we rigorously show that itinerant ferromagnetism and Bose-Einstein condensation may coexist.