Breakdown of the Landau-Fermi liquid in Two Dimensions due to Umklapp Scattering

Interacting fermions on the half-filled honeycomb lattice with short-range repulsions have been suggested to host a variety of interesting many-body ground states, e.g., a topological Mott insulator. A number of recent studies of the spinless case in terms of exact diagonalization, the infinite density matrix renormalization group and the functional renormalization group, however, indicate a suppression of the topological Mott insulating phase in the whole range of interactio...

The Bethe-Salpeter equation is combined with the temperature-cutoff functional renormalization group approach to analyze the order parameter structure for the leading instabilities of the 2D t-t' Hubbard model. We find significant deviations from pure s-, d-, or p-wave forms, which is due to the frustration of antiferromagnetism at small and intermediate t'. With adding a direct antiferromagnetic spin-exchange coupling the eigenfunctions in the particle-hole channel have exte...

Attractive non-local interactions jointly with repulsive local interaction in a microscopic modelling of electronic Fermi liquids generate a competition between an enhancement of the static charge susceptibility---ultimately signalling charge instability and phase separation---and its correlation induced suppression. We analyse this scenario through the investigation of the extended Hubbard model on a two-dimensional square lattice, using the spin rotation invariant slave-bos...

We study the two-dimensional square lattice Hubbard model for small to moderate interaction strengths $1\leq U/t\leq 4$ by means of the ladder dual fermion approach. The non-local correlations beyond dynamical mean-field theory lower the potential energy, lead to a maximum in the uniform susceptibility and induce a pseudogap in the density of states. While the self-energy exhibits precursors of a possible insulating phase linked to the appearance of long-range fluctuations, t...

We apply a wilsonian renormalization group approach to the system of electrons in a two-dimensional square lattice interacting near the saddle-points of the band, when the correlations at momentum ${\bf Q} = (\pi, \pi)$ prevail in the system. The detailed consideration of the spin degrees of freedom allows to discern the way in which the SU(2) spin invariance is preserved in the renormalization process. Regarding the spin correlations, we find two different universality class...

We present density-matrix renormalization group results for the ground state properties of two-leg Hubbard ladders. The half-filled Hubbard ladder is an insulating spin-gapped system, exhibiting a crossover from a spin-liquid to a band-insulator as a function of the interchain hopping matrix element. When the system is doped, there is a parameter range in which the spin gap remains. In this phase, the doped holes form singlet pairs and the pair-field and the "$4 k_F$" density...

We report the application of the density-matrix renormalization group method to a spatially anisotropic two-dimensional Hubbard model at half-filling. We find a deconfinement transition induced by the transverse hopping parameter $t_y$ from an insulator to a metal. Therefore, if $t_y$ is fixed in the metallic phase, increasing the interaction $U$ leads to a metal-to-insulator transition at a finite critical $U$. This is in contrast to the weak-coupling Hartree-Fock theory whi...

We study the electronic instabilities in a 2D Hubbard model where one of the dimensions has a finite width, so that it can be considered as a large array of coupled chains. The finite transverse size of the system gives rise to a discrete string of Fermi points, with respective electron fields that, due to their mutual interaction, acquire anomalous scaling dimensions depending on the point of the string. Using bosonization methods, we show that the anomalous scaling dimensio...

It is investigated, on the basis of the fluctuation exchange approximation, how the shape of the Fermi surface is modified in two-dimensional $t-t'-U$ Hubbard model at half filling as strength of the onsite Coulomb interaction $U$ is increased. The antiferromagnetic (AF) correlation length is shown to be enhanced as the Coulomb interaction get closer to the critical value $U_{\rm c}$ for the onset AF order. At the same time, the shape of the renormalized Fermi surface is defo...

We review magnetic and superconducting instabilities in the t-t' Hubbard model on the two-dimensional square lattice as obtained with functional one-loop renormalization group techniques. Special emphasis is put on ferromagnetic and triplet superconducting tendencies that could be relevant to the triplet superconductor Sr2RuO4.