复曲面编码中拓扑和边界变化引起的拓扑相变
Topological Phase Transitions Induced by Varying Topology and Boundaries in the Toric Code
摘要：
物质的拓扑相的一个重要特征是定义它们的基础流形的拓扑。在本文中，我们提出了敏感性的物质相的底层拓扑结构，通过研究的相变诱导由于边界条件的变化。我们声称，这些相变是伴随着在激发空间中的对称性破缺，并获得进一步的洞察力，我们分析了各种签名，如基态简并，拓扑纠缠熵，同时引入开环运营商的期望值有效地捕捉相变。此外，我们扩展到一个开放的量子设置的分析，通过定义有效的崩溃运营商，其动力学冷却系统到不同的拓扑有序的稳定状态。我们表明，这种稳定状态之间的相变有效地捕获的期望值的开环运营商。
英文摘要：
One of the important characteristics of topological phases of matter is the topology of the underlying manifold on which they are defined. In this paper, we present the sensitivity of such phases of matter to the underlying topology, by studying the phase transitions induced due to the change in the boundary conditions. We claim that these phase transitions are accompanied by broken symmetries in the excitation space and to gain further insight we analyze various signatures like the ground state degeneracy, topological entanglement entropy while introducing the open-loop operator whose expectation value effectively captures the phase transition. Further, we extend the analysis to an open quantum setup by defining effective collapse operators, the dynamics of which cool the system to different topologically ordered steady states. We show that the phase transition between such steady states is effectively captured by the expectation value of the open-loop operator.
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