论文标题
拓扑绝缘子和关联的$ \ mathbb {z} $中的近似对称和保护法
Approximate symmetries and conservation laws in topological insulators and associated $\mathbb{Z}$-invariants
论文作者
论文摘要
带有时间反转对称性和/或粒子孔对称性的固态系统通常只有$ \ mathbb {z} _2 $ - 可估算的强不变性剂，尚不知道一般的本地公式。对于参数的物理相关值，可能存在近似对称性或几乎保守的可观察物，例如具有小rashba耦合的量子自旋系统中的旋转。它在一般环境中显示了如何定义源自复杂理论的强大整数强的强不变性，例如旋转Chern数字，而Chern数字则等于$ \ Mathbb {z} _2 $ invariants。此外，可以使用光谱定位器的扭曲版本计算这些整数不变性。
Solid state systems with time reversal symmetry and/or particle-hole symmetry often only have $\mathbb{Z}_2$-valued strong invariants for which no general local formula is known. For physically relevant values of the parameters, there may exist approximate symmetries or almost conserved observables, such as the spin in a quantum spin Hall system with small Rashba coupling. It is shown in a general setting how this allows to define robust integer-valued strong invariants stemming from the complex theory, such as the spin Chern numbers, which modulo $2$ are equal to the $\mathbb{Z}_2$-invariants. Moreover, these integer invariants can be computed using twisted versions of the spectral localizer.
