对称性强制拓扑奇偶性：重新审视超越胞元对称作用的 $2\mathbb{Z}$ 分类
Symmetry-enforced topological parity: revisiting $2\mathbb{Z}$ classifications beyond cellwise symmetry actions
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中文总结 AI 辅助
本文研究动量依赖对称性作用如何将拓扑绝缘体和超导体的 $2\mathbb{Z}$ 分类从偶整数约束变为奇整数约束，推导奇偶关系，并区分三种实现情况，揭示局域性对拓扑数的限制。
中文摘要 AI 辅助
动量依赖的对称性作用可以将拓扑绝缘体和超导体的 $2\mathbb{Z}$ 分类中的偶整数约束转变为奇整数约束，而不改变对称性代数。对于最高四维空间中的内部对称性和二阶晶体对称性，我们推导了带隙哈密顿量的陈数或绕数与其动量依赖反幺正对称矩阵的拓扑不变量之间的奇偶关系。每当对称性作用强制奇偶性时，任何保持对称性的带隙相必须是拓扑非平凡的。以胞元作用（由固定单位胞基中的动量无关矩阵表示）作为参考，我们确定局域性如何约束奇数拓扑数的实现。显式模型构造和不可行定理区分了三种情况：奇数值可由有限范围对称性作用实现，可由指数衰减的准局域作用实现但不能由有限范围作用实现，或在有限维布洛赫系统中不可能实现。
英文摘要
Momentum-dependent symmetry actions can turn the even-integer constraint of a $2\mathbb{Z}$ classification of topological insulators and superconductors into an odd-integer constraint without changing the symmetry algebra. For internal and order-two crystalline symmetries in up to four spatial dimensions, we derive parity relations between the Chern or winding number of a gapped Hamiltonian and topological invariants of its momentum-dependent antiunitary symmetry matrices. Whenever the symmetry action enforces odd parity, any symmetry-preserving gapped phase must be topologically nontrivial. Using cellwise actions, which are represented by momentum-independent matrices in a fixed unit-cell basis, as a reference, we determine how locality constrains the realization of odd topological numbers. Explicit model constructions and no-go theorems distinguish three cases: odd values can be realized by finite-range symmetry actions, can be realized by exponentially decaying quasilocal actions but not by finite-range actions, or are impossible in finite-dimensional Bloch systems.
发表机构
- Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息中心）
机构由 AI 辅助整理，请以论文原文为准。
