论文标题
受耗散量子系统中转移的Sublattice对称性保护的拓扑阶段
Topological phases protected by shifted sublattice symmetry in dissipative quantum systems
论文作者
论文摘要
可以根据Gorini-Kossakowski-Sudarshan-Lindblad方程与Schrödinger方程中的非热汉密尔顿人之间的lindbladian之间的对应关系对量子系统的耗散动力学进行分类。虽然将普通的非热汉密顿人分为38个对称类别，但先前的研究表明，由于物理限制，林格拉德人被归类为10个对称类别。但是，在这项工作中，我们基于转移的Sublattice Symmetry（SLS）推出了Lindbladians的拓扑分类，这可以增加Lindbladians的对称类别的数量。我们介绍了转移的SLS，以便Lindbladian可以保留这种对称性并扮演与SLS相同的拓扑分类角色。为了进行验证，我们构建了一个耗散量子系统保留SLS的模型，并确认了受移位SL保护的边缘状态的存在。此外，还讨论了SLS受保护的边缘状态的存在与可观察数量的动力学之间的关系。
Dissipative dynamics of quantum systems can be classified topologically based on the correspondence between the Lindbladian in the Gorini-Kossakowski-Sudarshan-Lindblad equation and the non-Hermitian Hamiltonian in the Schrödinger equation. While general non-Hermitian Hamiltonians are classified into 38 symmetry classes, previous studies have shown that the Lindbladians are classified into 10 symmetry classes due to a physical constraint. In this work, however, we unveil a topological classification of Lindbladians based on shifted sublattice symmetry (SLS), which can increase the number of symmetry classes for the Lindbladians. We introduce shifted SLS so that the Lindbladian can retain this symmetry and take on the same role as SLS for the topological classification. For verification, we construct a model of a dissipative quantum system retaining shifted SLS and confirm the presence of edge states protected by shifted SLS. Moreover, the relationship between the presence of shifted SLS protected edge states and the dynamics of an observable quantity is also discussed.
