论文标题
将晶格转换为网络：海森堡模型及其与远程相互作用的概括
Converting Lattices into Networks: The Heisenberg Model and Its Generalizations with Long-Range Interactions
论文作者
论文摘要
在本文中，我们将晶格配置转换为具有不同链接模式的网络，并考虑具有任意数量相互作用粒子对的网络上的模型。我们通过揭示统一组的Casimir操作员与置换组的共轭级操作员之间的关系来解决Heisenberg模型。我们通过这种关系概括了海森堡模型，并提供了一系列可解决的模型。此外，通过数值计算海森堡模型的特征值和具有不同链接的网络上的随机步行，我们表明在晶格配置上具有与更多粒子对之间相互作用的晶格配置的系统具有更高的特征性二变型。讨论了晶格模型的特征状态的最高退化。
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.
