The bilinear-biquadratic model on the complete graph
Statistical Mechanics
2018-02-13 v2 Mathematical Physics
math.MP
Quantum Physics
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 su(3) and su(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.
Keywords
Cite
@article{arxiv.1709.06602,
title = {The bilinear-biquadratic model on the complete graph},
author = {Dávid Jakab and Gergely Szirmai and Zoltán Zimborás},
journal= {arXiv preprint arXiv:1709.06602},
year = {2018}
}