We explore the possibilities of using the fermionic functional renormalization group to compute the phase diagram of systems with competing instabilities. In order to overcome the ubiquituous divergences encountered in RG flows, we propose to use sym
metry breaking counterterms for each instability, and employ a self-consistency condition for fixing the counterterms. As a validity check, results are compared to known exact results for the case of one-dimensional systems. We find that whilst one-dimensional peculiarities, in particular algebraically decaying correlation functions, can not be reproduced, the phase boundaries are reproduced accurately, encouraging further explorations for higher-dimensional systems.
We use the functional renormalization group to analyze the temperature dependence of the quasi-particle scattering rates in the two-dimensional Hubbard model below half-filling. Using a band structure appropriate to overdoped Tl2Ba2CuO(6+x) we find a
strongly angle dependent term linearly dependent on temperature which derives from an increasing scattering vertex as the energy scale is lowered. This behavior agrees with recent experiments and confirms earlier conclusions on the origin of the breakdown of the Landau Fermi liquid near the onset of superconductivity.
We present a functional renormalization group analysis of superconductivity in the ground state of the attractive Hubbard model on a square lattice. Spontaneous symmetry breaking is treated in a purely fermionic setting via anomalous propagators and
anomalous effective interactions. In addition to the anomalous interactions arising already in the reduced BCS model, effective interactions with three incoming legs and one outgoing leg (and vice versa) occur. We accomplish their integration into the usual diagrammatic formalism by introducing a Nambu matrix for the effective interactions. From a random-phase approximation generalized through use of this matrix we conclude that the impact of the 3+1 effective interactions is limited, especially considering the effective interactions important for the determination of the order parameter. The exact hierarchy of flow equations for one-particle irreducible vertex functions is truncated on the two-particle level, with higher-order self-energy corrections included in a scheme proposed by Katanin. Using a parametrization of effective interactions by patches in momentum space, the flow equations can be integrated numerically to the lowest scales without encountering divergences. Momentum-shell as well as interaction-flow cutoff functions are used, including a small external field or a large external field and a counterterm, respectively. Both approaches produce momentum-resolved order parameter values directly from the microscopic model. The size of the superconducting gap is in reasonable agreement with expectations from other studies.
We consider extended Hubbard models with repulsive interactions on a Honeycomb lattice and the transitions from the semi-metal phase at half-filling to Mott insulating phases. In particular, due to the frustrating nature of the second-neighbor repuls
ive interactions, topological Mott phases displaying the quantum Hall and the quantum spin Hall effects are found for spinless and spinful fermion models, respectively. We present the mean-field phase diagram and consider the effects of fluctuations within the random phase approximation (RPA). Functional renormalization group analysis also show that these states can be favored over the topologically trivial Mott insulating states.
We calculate the Landau interaction function f(k,k) for the two-dimensional t-t Hubbard model on the square lattice using second and higher order perturbation theory. Within the Landau-Fermi liquid framework we discuss the behavior of spin and charge
susceptibilities as function of the onsite interaction and band filling. In particular we analyze the role of elastic umklapp processes as driving force for the anisotropic reduction of the compressibility on parts of the Fermi surface.
