The bilinear–biquadratic model on the complete graph. (8th February 2018)

• Record Type: Journal Article
• Authors: Jakab, Dávid; Szirmai, Gergely; Zimborás, Zoltán
• Is Part Of: Journal of physics. Volume 51:Number 10(2018)
• Publication Date: 2018-02-08
• Subjects: magnetism -- bilinear–biquadratic model -- representation theory; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aaa92b
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We study the spin-1 bilinear–biquadratic model on the complete graph of N sites, i.e. when each spin is interacting with every other spin with the same strength. Because of its complete permutation invariance, this Hamiltonian can be rewritten as the linear combination of the quadratic Casimir operators of s u (3) and s u (2). Using group representation theory, we explicitly diagonalize the Hamiltonian and map out the ground-state phase diagram of the model. Furthermore, the complete energy spectrum, with degeneracies, is obtained analytically for any number of sites.