Does a pole in the self-energy imply a violation of the Luttinger theorem?
Abstract
Luttinger theorem relates Fermi surface volume to electron density per spin n. It holds in an arbitrary Fermi liquid but is widely believed to break when a fermionic self-energy has a pole. We show that this is not necessarily the case. As an example, we consider a fermionic system consisting of two gapped bands, originating from a self-energy Σ(ω, k) with a pole, and a narrow residual quasiparticle band crossing ω=0, with a small residue Z ≪ 1 (a residual Fermi liquid). We consider Model I, in which Z also renormalizes quasiparticle bandwidth W to ZW and Model II, in which W remains unrenormalized. The Green's function for such a system G(ω, k) contains two zeros and three poles --- one from the quasiparticle band and two from the gapped bands. Yet, we show that in Model I, the Luttinger-Ward analysis is fully applicable for any Z >0, and the results are exactly the same as if the gapped bands did not exist. For Model II, the Luttinger-Ward analysis recovers once Z exceeds some critical value, which depends on fermionic density.
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BibTeX
@misc{abanov2026does,
title = {{Does a pole in the self-energy imply a violation of the Luttinger theorem?}},
author = {Artem Abanov and Andrey Chubukov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04663},
eprint = {2610.04663},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04663},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Does a pole in the self-energy imply a violation of the Luttinger theorem?
AU - Artem Abanov
AU - Andrey Chubukov
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04663
UR - https://arxiv.org/abs/2610.04663
AB - Luttinger theorem relates Fermi surface volume to electron density per spin n. It holds in an arbitrary Fermi liquid but is widely believed to break when a fermionic self-energy has a pole. We show that this is not necessarily the case. As an example, we consider a fermionic system consisting of two gapped bands, originating from a self-energy Σ(ω, k) with a pole, and a narrow residual quasiparticle band crossing ω=0, with a small residue Z ≪ 1 (a residual Fermi liquid). We consider Model I, in which Z also renormalizes quasiparticle bandwidth W to ZW and Model II, in which W remains unrenormalized. The Green's function for such a system G(ω, k) contains two zeros and three poles --- one from the quasiparticle band and two from the gapped bands. Yet, we show that in Model I, the Luttinger-Ward analysis is fully applicable for any Z >0, and the results are exactly the same as if the gapped bands did not exist. For Model II, the Luttinger-Ward analysis recovers once Z exceeds some critical value, which depends on fermionic density.
ER -