Generic Mott-Hubbard phase diagram for extended Hubbard models without Umklapp scattering

TL;DR

This study maps the ground-state phase diagram of the 1/r-Hubbard model at half-filling, revealing distinct phases and continuous transitions, emphasizing the robustness of the Mott transition without Umklapp scattering.

Contribution

It provides a comprehensive phase diagram for the 1/r-Hubbard model without Umklapp scattering, highlighting the nature of phase transitions and the stability of the Mott transition.

Findings

Identified three main phases: Luttinger liquid, Mott-Hubbard insulator, charge-density-wave insulator.

Found that phase transitions are continuous up to moderate interaction strengths.

Demonstrated that short-range interactions do not qualitatively alter the Mott transition.

Abstract

We determine the ground-state phase diagram for the 1/r-Hubbard model with repulsive nearest-neighbor interaction at half band-filling using the density-matrix renormalization group (DMRG) method. Due to the absence of Umklapp cattering, the phase diagram displays finite regions for the three generic phases, namely, a Luttinger liquid metal for weak interactions, a Mott-Hubbard insulator for dominant Hubbard interactions, and a charge-density-wave insulator for dominant nearest-neighbor interactions. Up to moderate interactions strengths, the quantum phase transitions between the metallic and insulating phases are continuous, i.e., the gap opens continuously as a function of the interaction strength. We conclude that generic short-range interactions do not change the nature of the Mott transition qualitatively.