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arXiv · 2305.02341

Failure of Topological Invariants in Strongly Correlated Matter

Jinchao Zhao·Peizhi Mai·Barry Bradlyn·Philip Phillips
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Abstract

We show exactly that standard `invariants' advocated to define topology for non-interacting systems deviate strongly from the Hall conductance whenever the excitation spectrum contains zeros of the single-particle Green function, $G$, 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, $h(\bb k)$, with $G^{-1}$ in the current operator, thereby laying plain why perturbative arguments fail.

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Jinchao Zhao, Peizhi Mai, Barry Bradlyn, Philip Phillips. 2023-05-03. Failure of Topological Invariants in Strongly Correlated Matter. https://doi.org/10.1103/physrevlett.131.106601

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