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

Abstract

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.

15 pages, 17 figures

References in corpus (13)

• Fermi surface and van Hove singularities in the itinerant metamagnet Sr3Ru2O7
• Antiferromagnetism and the gap of a Mott insulator: Results from analytic continuation of the self-energy
• Universality Classes of Metal-Insulator Transitions in Strongly Correlated Electron Systems and Mechanism of High-Temperature Superconductivity
• Phase separation in the Hubbard model
• Quantum and Topological Criticalities of Lifshitz Transition in Two-Dimensional Correlated Electron Systems
• First direct observation of the Van Hove singularity in the tunneling spectra of cuprates
• Proximity of the Superconducting Dome and the Quantum Critical Point in the Two-Dimensional Hubbard Model
• Paramagnon-induced dispersion anomalies in the cuprates
• Field-induced quantum critical route to a Fermi liquid in high-temperature superconductors
• Thermodynamics of the Quantum Critical Point at Finite Doping in the 2D Hubbard Model: A Dynamical Cluster Approximation Study
• Quantum Metamagnetic Transitions Induced by Changes in Fermi-Surface Topology -Applications to a Weak Itinerant-Electron Ferromagnet;ZrZn_2
• Non-Fermi liquid signatures in the Hubbard Model due to van Hove singularities
• Quantum critical "opalescence" around metal-insulator transitions

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