Lifshitz Transition in the Two Dimensional Hubbard Model

TL;DR

This study uses advanced quantum Monte Carlo simulations to identify Lifshitz transitions in the 2D Hubbard model, revealing how Fermi surface topology changes influence pseudogap formation and density of states near critical points.

Contribution

First numerical demonstration of Lifshitz transition in the 2D Hubbard model with detailed analysis of Fermi surface topology and density of states effects.

Findings

Lifshitz transition points linked to Fermi surface topology change

Van Hove singularity crosses the Fermi level at critical doping

Temperature dependence of pairing susceptibility differs from traditional scenarios

Abstract

Using large-scale dynamical cluster quantum Monte Carlo simulations, we study the Lifshitz transition of the two dimensional Hubbard model with next-nearest-neighbor hopping ($t'$), chemical potential and temperature as control parameters. At $t'\le0$, we identify a line of Lifshitz transition points associated with a change of the Fermi surface topology at zero temperature. In the overdoped region, the Fermi surface is complete and electron-like; across the Lifshitz transition, the Fermi surface becomes hole-like and develops a pseudogap. At (or very close to) the Lifshitz transition points, a van Hove singularity in the density of states crosses the Fermi level. The van Hove singularity occurs at finite doping due to correlation effects, and becomes more singular when $t'$ becomes more negative. The resulting temperature dependence on the bare d-wave pairing susceptibility close to the Lifshitz points is significantly different from that found in the traditional van Hove scenarios. Such unambiguous numerical observation of the Lifshitz transition at $t'\le0$ extends our understanding of the quantum critical region in the phase diagram, and shines lights on future investigations of the nature of the quantum critical point in the two dimensional Hubbard model.