Failure of Topological Invariants in Strongly Correlated Matter
Failure of Topological Invariants in Strongly Correlated Matter
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强相关物质中拓扑不变量的失效
DOI：
10.1103/physrevlett.131.106601
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发表时间：
2023
影响因子：
8.6
通讯作者：
Phillips, Philip
中科院分区：
文献类型：
--
作者：
Zhao, Jinchao;Mai, Peizhi;Bradlyn, Barry;Phillips, Philip
我们确切地表明，每当激发谱包含单粒子格林函数的零时，就像一般强相关系统一样，用于定义非相互作用系统拓扑的标准“不变量”就会强烈偏离霍尔电导。也就是说，我们表明，如果化学势位于价带之上，则“不变量”甚至不需要进入导带，而只需穿越可能位于两个带之间的零带即可改变。由于这种过程不改变多体基态，霍尔电导保持固定。这种与霍尔电导的脱节是由于在当前算符内替换了哈密顿量，从而阐明了微扰论证失败的原因。
We show exactly that standard “invariants” advocated to define topology for noninteracting systems deviate strongly from the Hall conductance whenever the excitation spectrum contains zeros of the single-particle Green’s function,, as in general strongly correlated systems. Namely, we show that if the chemical potential sits atop the valence band, the “invariant” changes without even accessing the conduction band but by simply traversing the band of zeros that might lie between the two bands. Since such a process does not change the many-body ground state, the Hall conductance remains fixed. This disconnect with the Hall conductance arises from the replacement of the Hamiltonian,, within the current operator, thereby laying plain why perturbative arguments fail.