Breakdown of the Luttinger sum-rule at the Mott-Hubbard transition in the one-dimensional t1-t2 Hubbard model

TL;DR

This study uses the density-matrix renormalization-group method to analyze the Mott-Hubbard transition in a one-dimensional t1-t2 Hubbard model, revealing a breakdown of the Luttinger sum-rule and a transition to an insulating dimerized phase with incommensurate spin excitations.

Contribution

It demonstrates the decoupling of magnetic and charge excitations at strong coupling and characterizes the momentum distribution signatures of the Mott-Hubbard and incommensurate transitions.

Findings

Mott-Hubbard transition occurs between metallic and insulating dimerized phases.

Signatures of the transition are observable in the momentum distribution functions.

Incommensurate spin excitations emerge in the insulating phase.

Abstract

We investigate the momentum distribution function near the Mott-Hubbard transition in the one-dimensional t1-t2 Hubbard model (the zig-zag Hubbard chain), with the density-matrix renormalization-group technique. We show that for strong interactions the Mott-Hubbard transition occurs between the metallic-phase and an insulating dimerized phase with incommensurate spin excitations, suggesting a decoupling of magnetic and charge excitations not present in weak coupling. We illustrate the signatures for the Mott-Hubbard transition and the commensurate-incommensurate transition in the insulating spin-gapped state in their respective ground-state momentum distribution functions.