A quantum critical point is found in the phase diagram of the two-dimensional Hubbard model [Vidhyadhiraja et al., Phys. Rev. Lett. 102, 206407 (2009)]. It is due to the vanishing of the critical temperature associated with a phase-separation transition, and it separates the non-Fermi-liquid region from the Fermi liquid. Near the quantum critical point, the pairing is enhanced since the real part of the bare $d$ -wave pairing susceptibility exhibits an 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 quantum critical point using high-quality estimates of the self-energy obtained by direct analytic continuation of the self-energy from the continuous-time quantum Monte Carlo method. We focus mainly on a van Hove singularity 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 ${t}^{\ensuremath{'}}$ in the model. For comparison, we calculate the bare $d$ -wave pairing susceptibility for noninteracting models with the usual two-dimensional tight-binding dispersion and a hypothetical quartic dispersion. We find that neither model yields a van Hove singularity that completely describes the critical algebraic behavior of the bare $d$ -wave pairing susceptibility found in the numerical data. The resistivity, thermal conductivity, thermopower, and the Wiedemann-Franz law are examined in the Fermi liquid, marginal Fermi liquid, and pseudogap doping regions. A negative next-near-neighbor hopping ${t}^{\ensuremath{'}}$ increases the doping region with marginal Fermi liquid character. Both $T$ and negative ${t}^{\ensuremath{'}}$ are relevant variables for the quantum critical point, and both the transport and the displacement of the van Hove singularity with filling suggest that they are qualitatively similar in their effect.A quantum critical point is found in the phase diagram of the two-dimensional Hubbard model [Vidhyadhiraja et al., Phys. Rev. Lett. 102, 206407 (2009)]. It is due to the vanishing of the critical temperature associated with a phase-separation transition, and it separates the non-Fermi-liquid region from the Fermi liquid. Near the quantum critical point, the pairing is enhanced since the real part of the bare $d$-wave pairing susceptibility exhibits an 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 quantum critical point using high-quality estimates of the self-energy obtained by direct analytic continuation of the self-energy from the continuous-time quantum Monte Carlo method. We focus mainly on a van Hove singularity 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 ${t}^{\ensuremath{'}}$ in the model. For comparison, we calculate the bare $d$-wave pairing susceptibility for noninteracting models with the usual two-dimensional tight-binding dispersion and a hypothetical quartic dispersion. We find that neither model yields a van Hove singularity that completely describes the critical algebraic behavior of the bare $d$-wave pairing susceptibility found in the numerical data. The resistivity, thermal conductivity, thermopower, and the Wiedemann-Franz law are examined in the Fermi liquid, marginal Fermi liquid, and pseudogap doping regions. A negative next-near-neighbor hopping ${t}^{\ensuremath{'}}$ increases the doping region with marginal Fermi liquid character. Both $T$ and negative ${t}^{\ensuremath{'}}$ are relevant variables for the quantum critical point, and both the transport and the displacement of the van Hove singularity with filling suggest that they are qualitatively similar in their effect.

arXiv:1104.3261Physical Review BDec 12, 201129 citations

Quantum criticality in the two-dimensional Hubbard model

Mathias Pelz

Jul 10, 20260 citations

Quantum criticality and incipient phase separation in the thermodynamic properties of the Hubbard model

D. G Alanakis, E. K Hatami, J. M Oreno +1 more

Transport measurements on the cuprates suggest the presence of a quantum critical point (QCP) hiding underneath the superconducting dome near optimal hole doping. We provide numerical evidence in support of this scenario via a dynamical cluster quantum Monte Carlo study of the extended two-dimensional Hubbard model. Single-particle quantities, such as the spectral function, the quasi-particle weight and the entropy, display a crossover between two distinct ground states: a Fermi liquid at low filling and a nonFermi liquid with a pseudo-gap at high filling. Both states are found to cross over to a marginal Fermi-liquid state at higher temperatures. For finite next-nearest-neighbour hopping t � , we find a classical critical point at temperature Tc. This classical critical point is found to be associated with a phase-separation transition between a compressible Mott gas and an incompressible Mott liquid corresponding to the Fermi liquid and the pseudo-gap state, respectively. Since the critical temperature Tc extrapolates to zeroTransport measurements on the cuprates suggest the presence of a quantum critical point (QCP) hiding underneath the superconducting dome near optimal hole doping. We provide numerical evidence in support of this scenario via a dynamical cluster quantum Monte Carlo study of the extended two-dimensional Hubbard model. Single-particle quantities, such as the spectral function, the quasi-particle weight and the entropy, display a crossover between two distinct ground states: a Fermi liquid at low filling and a nonFermi liquid with a pseudo-gap at high filling. Both states are found to cross over to a marginal Fermi-liquid state at higher temperatures. For finite next-nearest-neighbour hopping t � , we find a classical critical point at temperature Tc. This classical critical point is found to be associated with a phase-separation transition between a compressible Mott gas and an incompressible Mott liquid corresponding to the Fermi liquid and the pseudo-gap state, respectively. Since the critical temperature Tc extrapolates to zero

Jan 1, 20150 citations

Transport properties of the infinite-dimensional Hubbard model

Thomas Pruschke, Mark Jarrell

Physica B Condensed MatterApr 1, 19943 citations

d

-wave pairing susceptibility exhibits an 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 quantum critical point using high-quality estimates of the self-energy obtained by direct analytic continuation of the self-energy from the continuous-time quantum Monte Carlo method. We focus mainly on a van Hove singularity 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 ${t}^{\ensuremath{'}}$ in the model. For comparison, we calculate the bare

d

-wave pairing susceptibility for noninteracting models with the usual two-dimensional tight-binding dispersion and a hypothetical quartic dispersion. We find that neither model yields a van Hove singularity that completely describes the critical algebraic behavior of the bare

d

-wave pairing susceptibility found in the numerical data. The resistivity, thermal conductivity, thermopower, and the Wiedemann-Franz law are examined in the Fermi liquid, marginal Fermi liquid, and pseudogap doping regions. A negative next-near-neighbor hopping ${t}^{\ensuremath{'}}$ increases the doping region with marginal Fermi liquid character. Both

T

and negative ${t}^{\ensuremath{'}}$ are relevant variables for the quantum critical point, and both the transport and the displacement of the van Hove singularity with filling suggest that they are qualitatively similar in their effect.