Unveiling Order behind Complexity: Coexistence of Ferromagnetism and Bose-Einstein Condensation
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.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.