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

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, identifying three representative phases. In the weak-coupling regime, the zero-frequency Green's function shows a branch-cut structure at the Fermi momentum, and the Luttinger integral accurately reflects the particle density. As the interaction increases, the spectral weight near the Fermi momentum is gradually suppressed. In the strong-coupling regime near half-filling, the singularity is progressively destroyed, accompanied by zeros in the real part of the Green's function. This leads to a non-Fermi-liquid metallic phase beyond the Luttinger liquid paradigm. While spectral weight remains at the original Fermi momentum, the singularity fades. Meanwhile, zeros with negligible spectral weight appear elsewhere, significantly affecting the integral. At half-filling, a single-particle gap opens, and the Green's function vanishes across momentum space, indicating the suppression of low-energy states, consistent with an insulating charge-density-wave phase. These results suggest that the breakdown of the Luttinger theorem arises from the interplay of interaction-driven excitation evolution and particle-hole symmetry breaking, leading to a continuous reconstruction of the generalized Fermi surface from topologically protected to correlation-driven.