Breakdown of the Luttinger sum rule within the Mott-Hubbard insulator

TL;DR

This paper investigates the breakdown of the Luttinger sum rule in a one-dimensional interacting fermion model, showing it fails in large-gap regimes but recovers as the Mott-Hubbard gap closes.

Contribution

The study demonstrates the conditions under which the Luttinger sum rule breaks down and recovers in a one-dimensional Mott insulator model with extended hopping.

Findings

Sum rule breaks down at large interaction strength V.

Sum rule recovers as the Mott-Hubbard gap vanishes.

Finite-size scaling analysis reveals the transition point.

Abstract

The validity of the Luttinger sum rule is investigated within the prototype tight-binding model of interacting fermions in one dimension, i.e., the t-V model including the next-nearest neighbor hopping t' in order to break the particle-hole symmetry. Scaling analysis of finite-system results at half-filling reveals evident breakdown of the sum rule in the regime of large gap at V >> t, while the sum rule appears to recover together with vanishing of the Mott-Hubbard gap.