Year: 2026
Type: preprint
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 $Σ(ω, \mathbf{k})$ with a pole, and a narrow residual quasiparticle band crossing $ω=0$, with a small residue $Z \ll 1$ (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 $G(ω, \mathbf{k})$ 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.
Source: arXiv (Cornell University)
Authors: Abanov, Artem, Chubukov, Andrey
Institutions: Texas A&M University, University of Minnesota
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G2529518089, G7008355296
OpenAlex ID: W7220724789