Density waves and Cooper pairing on the honeycomb lattice

Motivated by the surge in research activities on graphene, we investigate instabilities of electrons on the honeycomb lattice, interacting by onsite and nearest-neighbor terms, using a renormalization group scheme. Near half band-filling, critical minimal interaction strengths are required for instabilities toward antiferromagnetic or charge-density wave order. Away from half filling, f-wave triplet pairing and d+id singlet pairing instabilities are found to emerge out of density-wave regimes.Comment: 4 pages, 3 figure

Influence of hopping selfenergy and quasiparticle degradation on the antiferromagnetic ordering in the bilayer honeycomb Hubbard model

We study the Hubbard model on the AB-stacked bilayer honeycomb lattice with a repulsive onsite interaction U in second order perturbation theory and in self-consistent random phase approximation. We determine the changes in the antiferromagnetic magnetic ordering tendencies due to the real and imaginary parts of the selfenergy at the band crossing points. In particular we present an estimate for the threshold value U* below which the magnetic order is endangered by the splitting of the quadratic band touching points into four Dirac points by an interaction-induced interlayer skew hopping. For most of the parameter space however, the quasiparticle degradation by the frequency-dependence of the sublattice-diagonal selfenergies and the Dirac-cone steepening are more essential for suppressing the AF ordering tendencies considerably. Our results might help to understand to understand the energy scales obtained in renormalization group treatments of the same model and shed light on recent quantum Monte Carlo investigations about the fate of the magnetic ordering down to lower U.Comment: 10 pages, 8 figure

Electron-doping versus hole-doping in the 2D t-t' Hubbard model

We compare the one-loop renormalization group flow to strong coupling of the electronic interactions in the two-dimensional t-t'-Hubbard model with t'=-0.3t for band fillings smaller and larger than half-filling. Using a numerical N-patch scheme (N=32...96) we show that in the electron-doped case with decreasing electron density there is a rapid transition from a d(x^2-y^2)-wave superconducting regime with small characteristic energy scale to an approximate nesting regime with strong antiferromagnetic tendencies and higher energy scales. This contrasts with the hole-doped side discussed recently which exhibits a broad parameter region where the renormalization group flow suggests a truncation of the Fermi surface at the saddle points. We compare the quasiparticle scattering rates obtained from the renormalization group calculation which further emphasize the differences between the two cases.Comment: 11 pages, 16 figure

Charge instabilities at the metamagnetic transition

We investigate instabilities in the charge channel in the vicinity of (meta-)magnetic transitions of itinerant electron systems. Based on a weak coupling analysis we argue that in a one-band $t$-$t'$ Hubbard model near the van Hove filling and dominant ferromagnetic fluctuations it is difficult to account for a microscopic mechanism for a d-wave Pomeranchuk deformation of the Fermi surface. A similar deformation has been considered for the metamagnetic transition in Sr$_3$Ru$_2$O$_7$. As an alternative we discuss the possibility of charge inhomogeneity on the nano scale. This extends the analogy of the metamagnetic transition to a liquid-gas transition.Comment: 4 pages, 2 figure

Efficient vertex parametrization for the constrained functional renormalization group for effective low-energy interactions in multiband systems

We describe an efficient approximation for the electron-electron interaction in the determination of the low-energy effective interaction in multiband lattice systems. By using ideas for channel decomposition, form-factor expansion and the truncated-unity technique we describe the interaction as arising from the non-local and orbital-dependent coupling of particle-hole and particle-particle bilinears formed by fields residing in the same one or two orbitals. This allows us to employ the constrained functional renormalization group (cfRG) with a suitable momentum and frequency discretization. The approach gives insights into the non-local screening of spin and charge interactions when bands away from the Fermi level are integrated out. Specifically, we compute the effective low-energy interactions in the low-energy target band of a three-band model with onsite and non-local bare interactions. We show that the cfRG adds important features to the effective target-band interaction that cannot be found using the constrained random phase approximation (cRPA).Comment: 20 pages, 9 figure

Instabilities of quadratic band crossing points

Using a functional renormalization group approach, we study interaction-driven instabilities in quadratic band crossing point two-orbital models in two dimensions, extending a previous study of Sun et al. [1]. The wavevector-dependence of the Bloch eigenvectors of the free Hamiltonian causes interesting instabilities toward spin nematic, quantum anomalous Hall and quantum spin Hall states. In contrast with other known examples of interaction-driven topological insulators, in the system studied here, the QSH state occurs at arbitrarily small interaction strength and for rather simple intra- and inter-orbital repulsions.Comment: 9 pages, 6 figures; additional information on the fRG method (section 3) and minor change

Ultracold fermions and the SU(N) Hubbard model

We investigate the fermionic SU(N) Hubbard model on the two-dimensional square lattice for weak to moderate interaction strengths using one-loop renormalization group and mean-field methods. For the repulsive case U>0 at half filling and small N the dominant tendency is towards breaking of the SU(N) symmetry. For N>6 staggered flux order takes over as the dominant instability, in agreement with the large-N limit. Away from half filling for N=3 the system rearranges the particle densities such that two flavors remain half filled by cannibalizing the third flavor. In the attractive case and odd N a full Fermi surface coexists with a superconductor in the ground state. These results may be relevant to future experiments with cold fermionic atoms in optical lattices.Comment: 4 pages, 3 figure

Exact diagonalization study of the trionic crossover and the trion liquid in the attractive three-component Hubbard model

We investigate the trion formation and the effective trionic properties in the attractive Hubbard model with three fermionic colors using exact diagonalization. The crossover to the trionic regime with colorless compound fermions upon increasing strength of the onsite attraction parameter U features smoothly evolving ground state properties and exhibits clear similarities to the BCS/BEC-crossover for two colors. In the excitation spectrum, there is a clear gap opening between a band of well-defined trions and excitations of broken-up trions at U_c ~ 1.8t. This picture remains the same away from the SU(3)-symmetric point. The spatial pairing correlations for colored Cooper pairs are compatible with a power-law at small attractions and change to an exponential decay above the trionic crossover. Furthermore, we show that the effective trionic liquid for U > U_c can be well modeled with spinless 'heavy' fermions interacting with a strong nearest neighbor repulsion.Comment: 9 pages, 8 figures, changed figure 6, fixed typos, added definitions, motivated choice of considered quantitie