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

We study Umklapp couplings and their renormalisation group flow for electrons in a two dimensional lattice. It is shown that the effective low energy Hamiltonian involves not only forward scattering, but also considerable nonforward umklapp scattering, when the electrons fill a substantial fraction of the valence band. The behaviour of these couplings under renormalisation group is studied. It is shown that they remain marginal. We conclude with the possible consequences of t...

Using a recently developed renormalization group method for fermionic superfluids, we determine conditions for d-wave superconductivity in the two-dimensional Hubbard model at moderate interaction strength, and we compute the pairing gap in the superconducting regime. A pairing instability signaled by a divergent flow in the Cooper channel leads to a superconducting state in all studied cases. The next-to-nearest neighbor hopping $t'$ plays a crucial role in the competition b...

Salmhofer [Commun. Math. Phys. 194, 249 (1998)] has recently developed a new renormalization group method for interacting Fermi systems, where the complete flow from the bare action of a microscopic model to the effective low-energy action, as a function of a continuously decreasing infrared cutoff, is given by a differential flow equation which is local in the flow parameter. We apply this approach to the repulsive two-dimensional Hubbard model with nearest and next-nearest ...

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...

We use a novel temperature-flow renormalization group technique to analyze magnetic and superconducting instabilities in the two-dimensional t-t' Hubbard model for particle densities close to the van Hove filling as a function of the next-nearest neighbor hopping t'. In the one-loop flow at the van Hove filling, the characteristic temperature for the flow to strong coupling is suppressed drastically around t'_c approx. -0.33t, suggesting a quantum critical point between d-wav...

The problem of weakly correlated electrons on a square lattice is formulated in terms of one-loop renormalization group. Starting from the action for the entire Brillouin zone (and not with a low-energy effective action) we reduce successively the cutoff $\Lambda$ about the Fermi surface and follow the renormalization of the coupling $U$ as a function of three energy-momenta. We calculate the intrinsic scale $T_{co}$ where the renormalization group flow crosses over from the ...

We derive an efficient and unbiased method for computing order parameters in correlated electron systems with competing instabilities. Charge, magnetic and pairing fluctuations above the energy scale of spontaneous symmetry breaking are taken into account by a functional renormalization group flow, while the formation of order below that scale is treated in mean-field theory. The method captures fluctuation driven instabilities such as $d$-wave superconductivity. As a first a...

We consider serious conceptual problems with the application of standard perturbation theory, in its zero temperature version, to the computation of the dressed Fermi surface for an interacting electronic system. In order to overcome these difficulties, we set up a variational approach which is shown to be equivalent to the renormalized perturbation theory where the dressed Fermi surface is fixed by recursively computed counterterms. The physical picture that emerges is that ...

Phase diagrams of the two-dimensional one-band t-t' Hubbard model are obtained within the two-patch and the temperature-cutoff many-patch renormalization group approach. At small t' and at van Hove band fillings antiferromagnetism dominates, while with increasing t' or changing filling antiferromagnetism is replaced by d-wave superconductivity. Near t'=t/2 and close to van Hove band fillings the system is unstable towards ferromagnetism. Away from van Hove band fillings this ...

We show that the concept of umklapp-scattering driven instabilities in one-dimensional systems can be generalized to arbitrary multiple umklapp-scattering processes at commensurate fillings given that the system has sufficiently longer range interactions. To this end we study the fundamental model system, namely interacting spinless fermions on a one-dimensional lattice, via a density matrix renormalization group approach. The instabilities are investigated via a new method a...