Violation of Luttinger's theorem in one-dimensional interacting fermions

TL;DR

This study uses the density matrix renormalization group to explore how strong interactions in one-dimensional fermion systems cause the breakdown of Luttinger's theorem, revealing a transition to a non-Fermi liquid phase with zeros in the Green's function.

Contribution

It demonstrates the violation of Luttinger's theorem in a one-dimensional interacting fermion model due to spectral weight suppression and the emergence of momentum-space zeros, expanding understanding of non-Fermi liquid phases.

Findings

Luttinger integral reflects particle density in weak coupling.

Spectral weight suppression near Fermi momentum with increasing interaction.

Emergence of zeros in Green's function indicating non-Fermi liquid behavior.

Abstract

Using the density matrix renormalization group method, we systematically investigate the evolution of the Luttinger integral in the one-dimensional generalized $t$-$V$ model as a function of filling and interaction strength, and identify three representative phases. In the weak-coupling regime, the zero-frequency Green's function exhibits a branch-cut structure at the Fermi momentum, and the Luttinger integral accurately reflects the particle density, indicating that the Luttinger theorem holds. As the interaction increases, the spectral weight near the Fermi momentum is gradually suppressed. Interestingly, in the strong coupling regime near half-filling, this singularity is progressively destroyed, accompanied by the emergence of momentum-space zeros in the real part of the Green's function, leading to a novel non-Fermi liquid metallic phase beyond the classic Luttinger liquid paradigm, where the Luttinger surface is no longer defined by a single singularity. While finite spectral weight remains at the original Fermi momentum, the singularity gradually diminishes. Meanwhile, zeros with negligible spectral weight appear away from this momentum, significantly affecting the integral. At exact half-filling, a single-particle gap opens, and the Green's function becomes nearly vanishing across the entire momentum space, indicating the complete suppression of low-energy electronic states consistent with the nature of an insulating charge-density-wave phase. These results suggest that the breakdown of the Luttinger theorem is not triggered by a single mechanism, but rather results from the interplay between interaction-driven evolution of excitation modes and the breaking of particle-hole symmetry, ultimately leading to a continuous reconstruction of the generalized Fermi surface from topologically protected to correlation-driven.