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arXiv:1308.0812 · Physical Review Letters

Fermi Condensation Near van Hove Singularities Within the Hubbard Model on the Triangular Lattice

Dmitry I. Yudin, Daniel Hirschmeier, Hartmut Hafermann, Olle Eriksson, Alexander I. Lichtenstein, Mikhail I. Katsnelson

Published Feb 20, 2014• 137 citations
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Abstract

The proximity of the Fermi surface to van Hove singularities drastically enhances interaction effects and leads to essentially new physics. In this work we address the formation of flat bands ("Fermi condensation") within the Hubbard model on the triangular lattice and provide a detailed analysis from an analytical and numerical perspective. To describe the effect we consider both weak-coupling and strong-coupling approaches, namely the renormalization group and dual fermion methods. It is shown that the band flattening is driven by correlations and is well pronounced even at sufficiently high temperatures, of the order of 0.1-0.2 of the hopping parameter. The effect can therefore be probed in experiments with ultracold fermions in optical lattices.

DOI
10.1103/physrevlett.112.070403

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The proximity of the Fermi surface to van Hove singularities drastically enhances interaction effects and leads to essentially new physics. In this work we address the formation of flat bands ("Fermi condensation") within the Hubbard model on the triangular lattice and provide a detailed analysis from an analytical and numerical perspective. To describe the effect we consider both weak-coupling and strong-coupling approaches, namely the renormalization group and dual fermion methods. It is shown that the band flattening is driven by correlations and is well pronounced even at sufficiently high temperatures, of the order of 0.1-0.2 of the hopping parameter. The effect can therefore be probed in experiments with ultracold fermions in optical lattices.
The pinning of the Fermi level to the Van Hove singularity and the formation of flat bands in the two-dimensional $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model is investigated by the renormalization group technique. The ``Van Hove'' scenario of non-Fermi-liquid behavior for high-Tc{T}_{c}Tc​ compounds can take place in a broad enough range of the hole concentrations. The results are in qualitative agreement with the recent angle-resolved photoemission spectroscopy data on La2CuO4\mathrm{L}{\mathrm{a}}_{2}\mathrm{C}\mathrm{u}{\mathrm{O}}_{4}La2​CuO4​.
We consider the electronic and magnetic properties of the Hubbard model on a square lattice with the Fermi level near van Hove singularity and the ratio of the next-nearest-neighbor and nearest-neighbor hoppings t′/t=−0.45t'/t=-0.45t′/t=−0.45, which favours the ferromagnetic instability. We find, that a self-consistent consideration of the ferromagnetic fluctuations within the D-TRILEX approach results in the splitting of the electronic spectral function at low temperatures. This splitting exhibits only a weak momentum dependence, and only one of the split bands crosses the Fermi level. As a result, the Fermi surface itself remains unsplit, but its area increases, reflecting the presence of non-Fermi-liquid electronic excitations. We show that both the self-consistent account of the non-local contributions to the electronic self-energy and the proper treatment of electron interaction vertices in D-TRILEX are important to obtain this behaviour.
We describe the enhanced magnetic transition temperatures Tc{T}_{c}Tc​ of two-component fermions in three-dimensional layered Lieb lattices, which are created in cold-atom experiments. We determine the phase diagram at half filling using the dynamical mean-field theory. The dominant mechanism of enhanced Tc{T}_{c}Tc​ gradually changes from the ($\ensuremath{\delta}$-functional) flat-band to the (logarithmic) Van Hove singularity as the interlayer hopping increases. We elucidate that the interaction induces an effective flat-band singularity from a dispersive flat (or narrow) band. We offer a general analytical framework for investigating the singularity effects, where a singularity is treated as one parameter in the density of states. This framework provides a unified description of the singularity-induced phase transitions, such as magnetism and superconductivity, where the weight of the singularity characterizes physical quantities. This treatment of the flat-band provides the transition temperature and magnetization as a universal form (i.e., including the Lambert function). We also elucidate a specific feature of the magnetic crossover in magnetization at finite temperatures.
Abstract We investigate magnetic correlation in the triangular lattice Hubbard model using determinant quantum Monte Carlo simulations. Focusing on the role of next-nearest-neighbor hopping t ′ and electron filling 〈 n 〉, we demonstrate that regions of high density of states, particularly near van Hove singularity (VHS) points, significantly enhance short-range ferromagnetic correlations as measured by the uniform spin susceptibility χ (Γ). Specifically, χ (Γ), quantifying ferromagnetic fluctuations, is amplified at fillings corresponding to the VHS for a given t ′ . Increasing the on-site Coulomb repulsion U further strengthens these ferromagnetic correlations, with a more pronounced effect at lower temperatures, and the observed ferromagnetic correlations are found to be short-ranged. Conversely, near half-filling 〈 n 〉 = 1.0, larger t ′ values promote antiferromagnetic (AFM) fluctuations, evidenced by an increase in χ ( K ). Our results reveal that t ′ and filling act as effective tuning parameters for manipulating the competition between ferromagnetic and AFM fluctuations in the triangular lattice.
We examine the quasiparticle lifetime and spectral weight near the Fermi surface in the two-dimensional Hubbard model. We use the FLEX approximation to self-consistently generate the Matsubara Green's functions and then we analytically continue to the real axis to obtain the quasiparticle spectral functions. We compare the spectral functions found in the nearest neighbor hopping only Hubbard model with those found when second neighbor hopping is included. This separates the effects of nesting, the Van Hove singularity and the short-ranged antiferromagnetic correlations. The quasiparticle scattering rate is enhanced along the (0,pi) to (pi,pi) Brillouin zone diagonal. When the density is close to half-filling these 'hot-spots' lie on the Fermi surface and the scattering rate increases with decreasing temperature. For the next-nearest neighbor hopping scenario we observe a large range of doping where there is no antiferromagnetism but the scattering rate has a linear temperature dependence. On decreasing the interaction this non-Fermi liquid behavior is confined to doping levels where the Fermi energy lies near to the Van Hove singularity. We conclude that the 'hot-spots' are associated with the antiferromagnetic phase transition while the linear temperature dependence of the scattering rate is associated with the Van Hove singularity.
We investigate the possibility of ferromagnetic ordering in the nondegenerate Hubbard model on the face-centered cubic lattice within the functional renormalization group technique using temperature as a scale parameter. We assume the relations between nearest, next-nearest, and next-next-nearest hopping parameters providing higher-order (giant) van Hove singularity of the density of states. The ferromagnetic instability formation with lowering temperature is described consistently in the one-loop approximation for a one-particle irreducible vertex of two-particle electron interaction. The chemical potential versus temperature phase diagrams are calculated. We find ferromagnetic order only for sufficiently strong divergence of the density of states and fillings in the vicinity of van Hove singularity. The obtained Curie temperature is more than an order of magnitude smaller than the results of the random-phase approximation. The main origin of the suppression of ferromagnetism is the screening of interaction in the particle-particle channel. We also do not find the pronounced tendency towards incommensurate order when the Fermi level is moved away from a van Hove singularity, such that the first-order quantum phase transitions from the ferro- to paramagnetic phase are obtained.