Green's function zeros, which can emerge only if correlation is strong, have been for long overlooked and believed to be devoid of any physical meaning, unlike Green's function poles. Here, we prove that Green's function zeros instead contribute on the same footing as poles to determine the topological character of an insulator. The key to the proof, worked out explicitly in two dimensions but easily extendable in three dimensions, is to express the topological invariant in terms of a quasiparticlethermal Green's function matrix G*(i ⠂, k) = 1/[i ⠂ - H*(⠂, k)], with Hermitian H*(⠂, k), by filtering out the positive-definite quasiparticle residue. In that way, the topological invariant is easily found to reduce to the Thouless, Kohmoto, Nightingale, and den Nijs formula for quasiparticles described by the noninteracting Hamiltonian H*(0, k). Since the poles of the quasiparticle Green's function G*(⠂, k) on the real frequency axis correspond to poles and zeros of the physical-particle Green's function G(⠂, k), both of them equally determine the topological character of an insulator.

Unified role of Green's function poles and zeros in correlated topological insulators / Blason, Andrea; Fabrizio, Michele. - In: PHYSICAL REVIEW. B. - ISSN 2469-9950. - 108:12(2023), pp. 1-10. [10.1103/physrevb.108.125115]

Unified role of Green's function poles and zeros in correlated topological insulators

Blason, Andrea;Fabrizio, Michele
2023-01-01

Abstract

Green's function zeros, which can emerge only if correlation is strong, have been for long overlooked and believed to be devoid of any physical meaning, unlike Green's function poles. Here, we prove that Green's function zeros instead contribute on the same footing as poles to determine the topological character of an insulator. The key to the proof, worked out explicitly in two dimensions but easily extendable in three dimensions, is to express the topological invariant in terms of a quasiparticlethermal Green's function matrix G*(i ⠂, k) = 1/[i ⠂ - H*(⠂, k)], with Hermitian H*(⠂, k), by filtering out the positive-definite quasiparticle residue. In that way, the topological invariant is easily found to reduce to the Thouless, Kohmoto, Nightingale, and den Nijs formula for quasiparticles described by the noninteracting Hamiltonian H*(0, k). Since the poles of the quasiparticle Green's function G*(⠂, k) on the real frequency axis correspond to poles and zeros of the physical-particle Green's function G(⠂, k), both of them equally determine the topological character of an insulator.
2023
108
12
1
10
125115
https://arxiv.org/abs/2304.08180
Blason, Andrea; Fabrizio, Michele
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/137371
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