Failure of Topological Invariants in Strongly Correlated Matter

Jinchao Zhao, Peizhi Mai, Barry Bradlyn, Philip Phillips

Research output: Contribution to journalArticlepeer-review


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, 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(k), with G-1 in the current operator, thereby laying plain why perturbative arguments fail.

Original languageEnglish (US)
Article number106601
JournalPhysical review letters
Issue number10
StatePublished - Sep 8 2023

ASJC Scopus subject areas

  • General Physics and Astronomy


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