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A quantum critical point (QCP), separating the non-Fermi liquid region fromthe Fermi liquid, exists in the phase diagram of the 2D Hubbard model[Vidhyadhiraja et. al, Phys. Rev. Lett. 102, 206407 (2009)]. Due to thevanishing of the critical temperature associated with a phase separationtransition, the QCP is characterized by a vanishing quasiparticle weight. Nearthe QCP, the pairing is enhanced since the real part of the bare d-wave p-psusceptibility exhibits algebraic divergence with decreasing temperature,replacing the logarithmic divergence found in a Fermi liquid [Yang et. al,Phys. Rev. Lett. 106, 047004 (2011)]. In this paper we explore thesingle-particle and transport properties near the QCP. We focus mainly on a vanHove singularity (vHS) coming from the relatively flat dispersion that crossesthe Fermi level near the quantum critical filling. The flat part of thedispersion orthogonal to the antinodal direction remains pinned near the Fermilevel for a range of doping that increases when we include a negativenext-near-neighbor hopping t' in the model. For comparison, we calculate thebare d-wave pairing susceptibility for non-interacting models with the usualtwo-dimensional tight binding dispersion and a hypothetical quartic dispersion.We find that neither model yields a vHS that completely describes the criticalalgebraic behavior of the bare d-wave pairing susceptibility. The resistivity,thermal conductivity, thermopower, and the Wiedemann-Franz Law are examined inthe Fermi liquid, marginal Fermi liquid, and pseudo-gap doping regions. Anegative next-near-neighbor hopping t' increases the doping region withmarginal Fermi liquid character. Both T and negative t' are relevant variablesfor the QCP, and both the transport and the motion of the vHS with fillingsuggest that they are qualitatively similar in their effect.

Role of the van Hove Singularity in the Quantum Criticality of the Hubbard Model