Converting Lattices into Networks: The Heisenberg Model and Its Generalizations with Long-Range Interactions

• URL: http://arxiv.org/abs/2012.12074v2
• Date: Sun, 3 Jan 2021 05:32:10 GMT
• Title: Converting Lattices into Networks: The Heisenberg Model and Its Generalizations with Long-Range Interactions
• Authors: Chi-Chun Zhou, Yao Shen, Yu-Zhu Chen, and Wu-Sheng Dai
• Abstract summary: 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 numerically calculate the eigenvalue of Heisenberg models and random walks on network with different numbers of links. The highest degeneracy of eigenstates of a lattice model is discussed.
• Score: 0.5949779668853554
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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