Role of the van Hove singularity in the quantum criticality of the Hubbard model

Abstract

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 Continuous-Time Quantum Monte Carlo. 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 ′ 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 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 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 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.

Anisotropic breakdown of Fermi liquid quasiparticle excitations in overdoped La2−xSrxCuO4

“…Such a temperature dependence has been reported 40,41 for La 2 À x À y R y Sr x CuO 4 with R ¼ Eu (y ¼ 0.2) or Nd (y ¼ 0.4) and dopants x ¼ 0.24 comparable to this study. As pointed out in recent numerical studies, the vicinity of the van-Hove singularity to the Fermi level should not be neglected and in concert with electron correlation this can also produce non-Fermi liquid behaviour 42,43 .…”

Lifshitz transition in the two-dimensional Hubbard model

“…We obtain high-quality estimates of the cluster self-energy Σ(K, ω) by employing the maximum entropy analytical continuation 45 (MEM) directly to the Matsubara-frequency self energies calculated from the DCA-CTQMC 25,46,47 . To perform MEM on the selfenergy the non-Hartree part of Σ(K, iω n ) must be normalize by U 2 χ σ,σ , where χ σ,σ = n σ n σ − n σ 2 = n σ (1−n σ ) is the local polarization of a single spin species σ.…”

“…It has been used to explain experimental data in high-T c cuprate superconductors 16,17 or heavy fermion systems 18 . Using large-scale dynamical cluster quantum Monte Carlo simulations 19 , a series of recent numerical works [20][21][22][23][24][25] mapped out the phase diagram of the two dimensional Hubbard model near the quantum critical filling. Particularly, the superconducting dome in the proximity to the quantum critical doping has been identified 23 .…”

Quantum criticality in NbFe2induced by zero carrier velocity

“…Such singularities have been studied extensively, both in weak coupling 1 and in the Hubbard model at strong coupling. [2][3][4] Nb 1−x Fe 2+x is a rare example of an itinerant transition metal intermetallic compound displaying antiferromagnetic quantum criticality. Its unusual magnetic behavior and its sensitivity to off-stoichiometry (Nb deficiency x) has been known for over two decades, 5,6 and its phase diagram and low temperature (T), small x behavior has recently been clarified.…”