77 research outputs found
d-wave superconductivity and Pomeranchuk instability in the two-dimensional Hubbard model
We present a systematic stability analysis for the two-dimensional Hubbard
model, which is based on a new renormalization group method for interacting
Fermi systems. The flow of effective interactions and susceptibilities confirms
the expected existence of a d-wave pairing instability driven by
antiferromagnetic spin fluctuations. More unexpectedly, we find that strong
forward scattering interactions develop which may lead to a Pomeranchuk
instability breaking the tetragonal symmetry of the Fermi surface.Comment: 4 pages (RevTeX), 4 eps figure
Exact integral equation for the renormalized Fermi surface
The true Fermi surface of a fermionic many-body system can be viewed as a
fixed point manifold of the renormalization group (RG). Within the framework of
the exact functional RG we show that the fixed point condition implies an exact
integral equation for the counterterm which is needed for a self-consistent
calculation of the Fermi surface. In the simplest approximation, our integral
equation reduces to the self-consistent Hartree-Fock equation for the
counterterm.Comment: 5 pages, 1 figur
Renormalized perturbation theory for Fermi systems: Fermi surface deformation and superconductivity in the two-dimensional Hubbard model
Divergencies appearing in perturbation expansions of interacting many-body
systems can often be removed by expanding around a suitably chosen renormalized
(instead of the non-interacting) Hamiltonian. We describe such a renormalized
perturbation expansion for interacting Fermi systems, which treats Fermi
surface shifts and superconductivity with an arbitrary gap function via
additive counterterms. The expansion is formulated explicitly for the Hubbard
model to second order in the interaction. Numerical soutions of the
self-consistency condition determining the Fermi surface and the gap function
are calculated for the two-dimensional case. For the repulsive Hubbard model
close to half-filling we find a superconducting state with d-wave symmetry, as
expected. For Fermi levels close to the van Hove singularity a Pomeranchuk
instability leads to Fermi surfaces with broken square lattice symmetry, whose
topology can be closed or open. For the attractive Hubbard model the second
order calculation yeilds s-wave superconductivity with a weakly momentum
dependent gap, whose size is reduced compared to the mean-field result.Comment: 18 pages incl. 6 figure
Magnetic and superconducting instabilities of the Hubbard model at the van Hove filling
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-wave pairing at moderate t'>t'_c and ferromagnetism for t'<t'_c. Upon
increasing the particle density in the latter regime the leading instability
occurs in the triplet pairing channel.Comment: 4 pages, to appear in Physical Review Letter
Superconducting and pseudogap phases from scaling near a Van Hove singularity
We study the quantum corrections to the Fermi energy of a two-dimensional
electron system, showing that it is attracted towards the Van Hove singularity
for a certain range of doping levels. The scaling of the Fermi level allows to
cure the infrared singularities left in the BCS channel after renormalization
of the leading logarithm near the divergent density of states. A phase of
d-wave superconductivity arises beyond the point of optimal doping
corresponding to the peak of the superconducting instability. For lower doping
levels, the condensation of particle-hole pairs due to the nesting of the
saddle points takes over, leading to the opening of a gap for quasiparticles in
the neighborhood of the singular points.Comment: 4 pages, 6 Postscript figures, the physical discussion of the results
has been clarifie
Fermi surface renormalization in Hubbard ladders
We derive the one-loop renormalization equations for the shift in the
Fermi-wavevectors for one-dimensional interacting models with four Fermi-points
(two left and two right movers) and two Fermi velocities v_1 and v_2. We find
the shift to be proportional to (v_1-v_2)U^2, where U is the Hubbard-U. Our
results apply to the Hubbard ladder and to the t_1-t_2 Hubbard model. The
Fermi-sea with fewer particles tends to empty. The stability of a saddle point
due to shifts of the Fermi-energy and the shift of the Fermi-wavevector at the
Mott-Hubbard transition are discussed.Comment: 5 pages, 4 Postscript figure
Marginal Fermi liquid behavior from 2d Coulomb interaction
A full, nonperturbative renormalization group analysis of interacting
electrons in a graphite layer is performed, in order to investigate the
deviations from Fermi liquid theory that have been observed in the experimental
measures of a linear quasiparticle decay rate in graphite. The electrons are
coupled through Coulomb interactions, which remain unscreened due to the
semimetallic character of the layer. We show that the model flows towards the
noninteracting fixed-point for the whole range of couplings, with logarithmic
corrections which signal the marginal character of the interaction separating
Fermi liquid and non-Fermi liquid regimes.Comment: 7 pages, 2 Postscript figure
Spontaneous symmetry breaking in the colored Hubbard model
The Hubbard model is reformulated in terms of different ``colored'' fermion
species for the electrons or holes at different lattice sites.
Antiferromagnetic ordering or d-wave superconductivity can then be described in
terms of translationally invariant expectation values for colored composite
scalar fields. A suitable mean field approximation for the two dimensional
colored Hubbard model shows indeed phases with antiferromagnetic ordering or
d-wave superconductivity at low temperature. At low enough temperature the
transition to the antiferromagnetic phase is of first order. The present
formulation also allows an easy extension to more complicated microscopic
interactions.Comment: 19 pages, 5 figure
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