Lifshitz transition in the two-dimensional Hubbard model

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 ′≤0, we identify a line of Lifshitz transition points associated with a change in 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 ′≤0 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. © 2012 American Physical Society.