arXiv 1504.059222015-04hep-thcond-mat.str-el

$3D$格点规范理论参数空间中的Toric类码模型

Toric code-like models from the parameter space of $3D$ lattice gauge theories

Miguel Jorge Bernabe Ferreira, Pramod Padmanabhan, Paulo Teotonio-Sobrinho

备注：: 12 pages, 7 figures. This paper is an extension of the one http://arxiv.org/abs/1310.8483. Slightly modified to make it more self-contained

摘要：

利用Kuperberg闭流形上的状态和构造方法，可以构造基于对合Hopf代数$\mathcal{A}$的$3D$格点规范理论的配分函数，其中群代数$\mathbb{C}G$是一个特例.在有边界的流形上进行这种构造可以得到传递矩阵。各种物理上感兴趣的哈密顿量可以从这些传递矩阵中得到，通过玩弄传递矩阵是其函数的参数。Kitaev的$2D$量子双哈密顿量可以从这些参数的特定值的转移矩阵中获得。在\cite{p1}中对这些模型进行了初步研究。在本文中，我们研究这个参数空间的其他区域，以获得一些新的和已知的模型。新的模型包括的哈密顿量的“部分”限制的量子双哈密顿量，通常是取消限制的激发。状态和构造允许参数取决于获得传递矩阵的位置，因此很自然地期望从它们中得到无序的哈密顿。因此，一组已知的模型由无序量子双哈密顿量组成。最后，我们得到了在磁场作用下的量子双哈密顿量，这在以前的文献中已经被用来研究拓扑序对扰动的稳定性。

英文摘要：

A state sum construction on closed manifolds á la Kuperberg can be used to construct the partition functions of $3D$ lattice gauge theories based on involutory Hopf algebras, $\mathcal{A}$, of which the group algebras, $\mathbb{C}G$, are a particular case. Transfer matrices can be obtained by carrying out this construction on a manifold with boundary. Various Hamiltonians of physical interest can be obtained from these transfer matrices by playing around with the parameters the transfer matrix is a function of. The $2D$ quantum double Hamiltonians of Kitaev can be obtained from such transfer matrices for specific values of these parameters. A initial study of such models has been carried out in \cite{p1}. In this paper we study other regions of this parameter space to obtain some new and known models. The new model comprise of Hamiltonians which "partially" confine the excitations of the quantum double Hamiltonians which are usually deconfined. The state sum construction allows for parameters depending on the position in obtaining the transfer matrices and thus it is natural to expect disordered Hamiltonians from them. Thus one set of known models consist of the disordered quantum double Hamiltonians. Finally we obtain quantum double Hamiltonians perturbed by magnetic fields which have been considered earlier in the literature to study the stability of topological order to perturbations.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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