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.
The Mott insulating phase of the parent compounds is frequently taken as starting point for the underdoped high-
Tc cuprate superconductors. In particular, the pseudogap state is often considered as deriving from the Mott insulator. In this work, we systematically investigate different weakly-doped Mott insulators on the square and triangular lattice to clarify the relationship between the pseudogap and Mottness. We show that doping a two-dimensional Mott insulator does not necessarily lead to a pseudogap phase. Despite its inherent strong-coupling nature, we find that the existence or absence of a pseudogap depends sensitively on non-interacting band parameters and identify the crucial role played by the van Hove singularities of the system. Motivated by a SU(2) gauge theory for the pseudogap state, we propose and verify numerically a simple equation that governs the evolution of characteristic features in the electronic scattering rate.
We theoretically study the two-dimensional metal that is coupled to critical magnons and features van Hove singularities on the Fermi surface. When there is only translationally invariant SYK-liked Yukawa interaction, van Hove points suppress the contribution from the part of the Fermi surface away from them, dominating and exhibiting non-Fermi-liquid behavior. When introducing disordered Yukawa coupling, it leads to a crossover from non-Fermi-liquid to marginal-Fermi-liquid, and the marginal-Fermi-liquid region exhibits the
Tln(1/T) specific heat and temperature-linear resistivity of strange metal. By solving the gap equation, we provide the critical temperature for superconductor induced by van Hove singularities and point out the possible emergence of pair-density-wave superconductor. Our theory may become a new mechanism for understanding non-Fermi-liquid or marginal-Fermi-liquid phenomenons.
The use of effective field theories to attack new and seemingly disparate problems has proliferated in the past several decades. In this thesis, we develop effective field theories for systems of fermionic quasiparticles possessing Fermi surfaces, with a particular focus on Fermi surfaces proximal to Van Hove singularities. Such systems are a fruitful source of complex and novel behavior in condensed matter physics. We begin with an overview of the renormalization group procedure at the heart of effective field theory by analyzing a simple example. We emphasize the concept that the RG relates the observables of one theory to those of another theory with precisely the same form but different numerical parameters. We also note the generality and extensibility of these concepts. We then apply this perspective to the study of quasiparticles with a round Fermi surface, employing the technique of binning the quasiparticle fields in momentum space to translate previous treatments into a more modern form. We next develop an effective field theory describing the excitations of modes around a Fermi surface with a Van Hove singularity. We resolve lingering questions about the presence of nonlocal interactions in similar models. We find a rich and complicated theory capable of describing deviations from typical Fermi liquid behavior that nonetheless displays some universal dependence on the interactions involving modes in the vicinity of the Van Hove point. We close with an analysis of the instabilities of this Van Hove effective field theory.
To clarify the origin of the pseudogap and strange metal states as well as their mutual relationship in cuprate superconductors, a comprehensive study on the spectral function, Fermi surface, resistivity and dynamical spin susceptivity of the Hubbard model on the square lattice has been conducted by means of the ladder dual-fermion approximation with an electron self-energy correction. It is found that the appearance of these two states requires that the characteristic hole concentration below which the Mott-Heisenberg and Slater mechanisms of electron localization occurs
pMS nearly coincides with the hole concentration where the Van Hove singularity (VHS) point is placed at the vicinity of the Fermi level. When this condition is met the VHS point is pinned at which the nesting condition of the antiferromagnetic (AFM) fluctuation is fulfilled almost everywhere on the Fermi surface in wide range of the hole concentration in a metallic state, i.e., the strange metal state. The spin fluctuation of the strange metal state is nearly quantum critical and the dynamical spin susceptivity is well described by overdamped spin wave having the
ω/T scaling with the relaxation rate at the Planckian limit. Because of these distinctive features of the strange metal state, the
k dependence of scattering rate of electrons is small and electrons behave as the marginal Fermi liquid, resulting in
T-linear resistivity. In contrast, the pseudogap state is magnetically in the renormalized classical regime and the pseudogap is formed near the X point where the nesting condition of the short-range AFM order is fulfilled.
We use a diagrammatic approach to study low-energy physics of a two-dimensional electron system where the Fermi level is near van Hove singularities in the energy spectrum. We find that in most regions of the ${\ensuremath{\epsilon}}_{F}\ensuremath{-}T$ phase diagram the system behaves as a normal Fermi liquid rather than a marginal Fermi liquid. Particularly, the imaginary part of the self-energy is much smaller than the excitation energy, which implies well-defined quasiparticle excitations, and single-particle properties are only weakly affected by the presence of the van Hove singularities. The relevance to high-temperature superconductivity is also discussed.