The bilinear–biquadratic model on the complete graph

Jakab, Dávid and Szirmai, Gergely and Zimborás, Zoltán (2018) The bilinear–biquadratic model on the complete graph. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 51. p. 105201. ISSN 1751-8113

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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.

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