论文标题
Floquet电路中的拓扑缺陷
Topological Defects in Floquet Circuits
论文作者
论文摘要
我们介绍了一个浮雕电路，描述了带有拓扑缺陷的驱动的Ising链。相应的门包括翻转旋转的缺陷以及明确实现Kramers-Wannier偶性转换的偶性缺陷。 Floquet Unitary Evolution操作员以这种缺陷的通勤通勤，但二元性缺陷并不统一，因为它投射了一半的州。我们给出了这些缺陷的两个应用。一种是在系统周围伸展的“空间状”缺陷存在下分析回报幅度。我们明确验证返回幅度与缺陷的融合规则一致。第二个应用是在存在抗周期性和双重性边界条件的“时间样”缺陷的情况下研究单一进化。我们表明，在后一种情况下出现了单个未配对的局部Majora零模式。我们明确构建了该操作员，该操作员充当该浮子电路的对称性。我们还为上述所有缺陷配置的几个站点系统的单个时间步骤介绍了纠缠熵的分析表达式。
We introduce a Floquet circuit describing the driven Ising chain with topological defects. The corresponding gates include a defect that flips spins as well as the duality defect that explicitly implements the Kramers-Wannier duality transformation. The Floquet unitary evolution operator commutes with such defects, but the duality defect is not unitary, as it projects out half the states. We give two applications of these defects. One is to analyze the return amplitudes in the presence of "space-like" defects stretching around the system. We verify explicitly that the return amplitudes are in agreement with the fusion rules of the defects. The second application is to study unitary evolution in the presence of "time-like" defects that implement anti-periodic and duality-twisted boundary conditions. We show that a single unpaired localized Majorana zero mode appears in the latter case. We explicitly construct this operator, which acts as a symmetry of this Floquet circuit. We also present analytic expressions for the entanglement entropy after a single time step for a system of a few sites, for all of the above defect configurations.
