标题： 颜色码中的部分任意子凝聚：哈密顿量方法 显示英文标题

标题： Partial Anyon Condensation in the Color Code: A Hamiltonian Approach

摘要： 格点哈密顿量可以在不同的拓扑相之间调节，被认为是理解拓扑相变物理机制的重要工具。 在本文中，我们引入了一个扰动的色码哈密顿量，其具有丰富的相结构，可以很好地匹配色码中的任意子凝聚机制。 我们考虑定义在一个三色可着色的六边形晶格上的色码模型，并在对应于晶格边的自旋之间添加伊辛相互作用。 我们表明，伊辛相互作用在色码中起到凝聚任意子的物理因子的作用。 特别是，对应于六边形晶格中三种不同的边颜色，我们考虑三种不同的耦合参数。 然后，通过调节对应边的伊辛相互作用的强度，我们能够凝聚不同颜色的任意子。 特别地，我们明确显示色码中一种任意子的凝聚会导致相变到拓扑码状态。 另一方面，通过凝聚两种类型的任意子，我们观察到一个相变到拓扑码的一个修改版本，在该版本中拓扑码的部分任意子被凝聚，我们称之为部分拓扑相。 我们得出上述结果的主要方法是基于主哈密顿量的一个合适的基变换，即我们的模型被映射到三个解耦的横向场伊辛模型，分别对应于三种颜色。 我们利用上述映射来分析字符串序参数的行为，作为拓扑序的非局部指示器。 我们引入了三个字符串序参数，可以很好地表征模型的不同相。 具体来说，我们使用字符串序参数对部分凝聚相进行了简单的描述。 显示英文摘要

摘要： Lattice Hamiltonians, which can be tuned between different topological phases, are known as important tools for understanding physical mechanism behind topological phase transitions. In this paper, we introduce a perturbed Color Code Hamiltonian with a rich phase structure which can be well matched to the mechanism of anyon condensation in the Color Code. We consider Color Code model defined on a three-colorable hexagonal lattice and add Ising interactions between spins corresponding to edges of the lattice. We show that Ising interactions play the role of physical factor for condensing anyons in the Color Code. In particular, corresponding to three different colors of edges in the hexagonal lattice, we consider three different coupling parameters. Then, we are able to condense anyons with different colors by tuning power of Ising interactions in the corresponding edges. In particular, we explicitly show that condensation of one type of anyons in the Color Code leads to a phase transition to the Toric Code state. On the other hand, by condensing two types of anyons, we observe a phase transition to a modified version of the Toric Code where partial set of anyons in the Toric Code are condensed and we call it a partially topological phase. Our main method for derivation of the above results is based on a suitable basis transformation on the main Hamiltonian in the sense that our model is mapped onto three decoupled transverse-field Ising models, corresponding to the three colors. We use the above mapping to analyze behavior of string order parameters as non-local indicators of topological order. We introduce three string order parameters that can well characterize different phases of the model. Specifically we give a simple description of the partially condensed phase by using string order parameters.