108 research outputs found
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
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
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 - 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 SrRuO. 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
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
Renormalization group flows into phases with broken symmetry
We describe a way to continue the fermionic renormalization group flow into
phases with broken global symmetry. The method does not require a
Hubbard-Stratonovich decoupling of the interaction. Instead an infinitesimally
small symmetry-breaking component is inserted in the initial action, as an
initial condition for the flow of the selfenergy. Its flow is driven by the
interaction and at low scales it saturates at a nonzero value if there is a
tendency for spontaneous symmetry breaking in the corresponding channel. For
the reduced BCS model we show how a small initial gap amplitude flows to the
value given by the exact solution of the model. We also discuss the emergence
of the Goldstone boson in this approach.Comment: 30 pages, LaTeX, 8 figure
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