A quantum critical point (QCP), separating the non-Fermi liquid region from
the Fermi liquid, exists in the phase diagram of the 2D Hubbard model
[Vidhyadhiraja et. al, Phys. Rev. Lett. 102, 206407 (2009)]. Due to the
vanishing of the critical temperature associated with a phase separation
transition, the QCP is characterized by a vanishing quasiparticle weight. Near
the QCP, the pairing is enhanced since the real part of the bare d-wave p-p
susceptibility 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 the
single-particle and transport properties near the QCP. We focus mainly on a van
Hove singularity (vHS) coming from the relatively flat dispersion that crosses
the Fermi level near the quantum critical filling. The flat part of the
dispersion orthogonal to the antinodal direction remains pinned near the Fermi
level for a range of doping that increases when we include a negative
next-near-neighbor hopping t' in the model. For comparison, we calculate the
bare d-wave pairing susceptibility for non-interacting models with the usual
two-dimensional tight binding dispersion and a hypothetical quartic dispersion.
We find that neither model yields a vHS that completely describes the critical
algebraic behavior of the bare d-wave pairing susceptibility. The resistivity,
thermal conductivity, thermopower, and the Wiedemann-Franz Law are examined in
the Fermi liquid, marginal Fermi liquid, and pseudo-gap doping regions. A
negative next-near-neighbor hopping t' increases the doping region with
marginal Fermi liquid character. Both T and negative t' are relevant variables
for the QCP, and both the transport and the motion of the vHS with filling
suggest that they are qualitatively similar in their effect.Comment: 15 pages, 17 figure
