The Elementary Excitation of Spin Lattice Models: The Quasiparticles of Gentile Statistics

Abstract

In this paper, we show that the elementary excitations of interacting spin lattice models, such as the Ising models, the Heisenberg models and the abelian Kitaev anyons, can be regarded as the quasiparticles of Gentile statistics. The advantage of the quasiparticle viewpoint is that eigenvalues and eigenstates of these models can be directly obtained by creating and annihilating Gentile quasiparticles. We provide the eigenstates and eigenvalues of d-dimensional Ising model with periodic boundary conditions. We also provide the eigenvalues of the Heisenberg models, the abelian Kitaev anyons, 2-dimensional and 3dimensional general spin lattice models. In addition, we point out that one kind of next nearest neighbor interacting models and more general interacting model may correspond to several kinds of quasiparticles of Gentile statistics.

Keywords: Gentile statistics, the connection matrix, Ising model