Topological defects in Floquet circuits
Topological defects in Floquet circuits
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Floquet 电路中的拓扑缺陷
作者：
Mao Tian Tan;Yifan Wang;A. Mitra
我们引入一个Floquet电路来描述具有拓扑缺陷的驱动Ising链。相应的门包括翻转自旋的缺陷以及明确实现Kramers-Wannier对偶变换的对偶缺陷。Floquet幺正演化算子与这种缺陷交换，但对偶缺陷不是幺正的，因为它投射出一半的状态。我们给出了这些缺陷的两个应用。一种是分析在系统周围存在“类空间”缺陷时的返回振幅。我们明确地验证了返回振幅与缺陷的融合规则是一致的。第二个应用是研究在“类时”缺陷的存在下，实现反周期和对偶扭曲的边界条件的幺正演化。我们发现，一个单一的未成对本地化马约拉纳零模式出现在后者的情况下。我们明确地构造这个操作员，它作为这个Floquet电路的对称。我们还提出了一个单一的时间步长后的纠缠熵的几个网站的系统，所有上述缺陷配置的解析表达式。
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.
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DOI：
10.1088/1751-8113/49/35/354001
发表时间：
2016-01
期刊：
Journal of Physics A: Mathematical and Theoretical
影响因子：
--
作者：
D. Aasen;R. Mong;P. Fendley
通讯作者：
D. Aasen;R. Mong;P. Fendley
具有经典可模拟算子置乱的量子电路。
影响因子：
8.6
作者：
Blake M
通讯作者：
Blake M
影响因子：
6.4
作者：
Preskill, John
通讯作者：
Preskill, John
DOI：
10.1103/physrevx.10.031066
发表时间：
2019-12
期刊：
arXiv: Strongly Correlated Electrons
影响因子：
--
作者：
Tianci Zhou;A. Nahum
通讯作者：
Tianci Zhou;A. Nahum
影响因子：
19.6
作者：
Lavasani, Ali;Alavirad, Yahya;Barkeshli, Maissam
通讯作者：
Barkeshli, Maissam