Converting Lattices into Networks: The Heisenberg Model and Its Generalizations with Long-Range Interactions
Abstract
In this paper, we convert the lattice configurations into networks with different modes of links and consider models on networks with arbitrary numbers of interacting particle-pairs. We solve the Heisenberg model by revealing the relation between the Casimir operator of the unitary group and the conjugacy-class operator of the permutation group. We generalize the Heisenberg model by this relation and give a series of exactly solvable models. Moreover, by numerically calculating the eigenvalue of Heisenberg models and random walks on network with different numbers of links, we show that a system on lattice configurations with interactions between more particle-pairs have higher degeneracy of eigenstates. The highest degeneracy of eigenstates of a lattice model is discussed.
Keywords
Cite
@article{arxiv.2012.12074,
title = {Converting Lattices into Networks: The Heisenberg Model and Its Generalizations with Long-Range Interactions},
author = {Chi-Chun Zhou and Yao Shen and Yu-Zhu Chen and Wu-Sheng Dai},
journal= {arXiv preprint arXiv:2012.12074},
year = {2021}
}