The properties of the two-dimensional Hubbard model with strong repulsion are studied under the condition that the Fermi surface passes through van Hove singularities. The upper critical field is calculated under conditions where there is no relaxation.
We examine the effects of a van Hove singularity (vHs) in the density of states (DOS) of a two dimensional, t−t′−U Hubbard model within the local approximation. Within our approximation the non-interacting Fermi surface is always retained away from half-filling; and we find that the vHs in the DOS survives, and for hole doping is nearly "pinned" to the Fermi level due to the enhancement of the effective mass, m∗. We discuss the electron-hole asymmetry of this phenomena and its relevance to the electron and hole doped cuprates. At optimal (hole) doping, with the Fermi level at the vHs, we find that the single particle damping rate Γ, and the resistivity ρdc, scale as T for moderately low temperatures (T≳100K), while for the electron doped system Γ and ρdc∼T2.
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 (${t}^{\ensuremath{'}}$), chemical potential, and temperature as control parameters. At ${t}^{\ensuremath{'}}\ensuremath{\le}0$, 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 ${t}^{\ensuremath{'}}$ 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 ${t}^{\ensuremath{'}}\ensuremath{\le}0$ 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.
The pinning of the Fermi level to the Van Hove singularity and the formation of flat bands in the two-dimensional $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model is investigated by the renormalization group technique. The ``Van Hove'' scenario of non-Fermi-liquid behavior for high-Tc compounds can take place in a broad enough range of the hole concentrations. The results are in qualitative agreement with the recent angle-resolved photoemission spectroscopy data on La2CuO4.
We study two-dimensional fermions with a short-range interaction in the presence of a Van Hove singularity. It is shown that this system can be consistently described by an effective field theory whose Fermi surface is subdivided into regions as defined by a factorization scale, and that the theory is renormalizable in the sense that all of the counterterms are well defined in the IR limit. The theory has the unusual feature that the renormalization-group equation for the coupling has an explicit dependence on the renormalization scale, much as in theories of Wilson lines. In contrast to the case of a round Fermi surface, there are multiple marginal interactions with nontrivial RG flow. The Cooper instability remains strongest in the BCS channel. We also show that the marginal Fermi-liquid scenario for the quasiparticle width is a robust consequence of the Van Hove singularity. Our results are universal in the sense that they do not depend on the detailed properties of the Fermi surface away from the singularity.
We determine the properties and leading instabilities of a spin liquid with a Fermi surface passing near a van Hove singularity. Our study is motivated by recent photoemission experiments on high-Tc cuprates in which it is found that for the optimally doped material the experimental Fermi surface passes near a van Hove singularity, while for underdoped materials, a pseudogap in the electron spectral function is formed in the vicinity of the van Hove point. We show theoretically that proximity to the van Hove singularity suppresses the inelastic scattering due to the gauge field and permits the formation of a d-wave RVB state in which the gap exists only near the van Hove points while finite regions of the Fermi surface remain gapless. This d-wave pairing provides a natural explanation of the pseudogap observed in photoemission. We also discuss the relation of the pseudogap observed in the spectral function to the pseudogaps observed in the magnetic susceptibility. \textcopyright{} 1996 The American Physical Society.