9 research outputs found
d-wave Superconductivity in the Hubbard Model
The superconducting instabilities of the doped repulsive 2D Hubbard model are
studied in the intermediate to strong coupling regime with help of the
Dynamical Cluster Approximation (DCA). To solve the effective cluster problem
we employ an extended Non Crossing Approximation (NCA), which allows for a
transition to the broken symmetry state. At sufficiently low temperatures we
find stable d-wave solutions with off-diagonal long range order. The maximal
occurs for a doping and the doping
dependence of the transition temperatures agrees well with the generic
high- phase diagram.Comment: 5 pages, 5 figure
ARPES Spectra of the Hubbard model
We discuss spectra calculated for the 2D Hubbard model in the intermediate
coupling regime with the dynamical cluster approximation, which is a
non-perturbative approach. We find a crossover from a normal Fermi liquid with
a Fermi surface closed around the Brillouin zone center at large doping to a
non-Fermi liquid for small doping. The crossover is signalled by a splitting of
the Fermi surface around the point of the 2D Brillouin zone, which
eventually leads to a hole-like Fermi surface closed around the point M. The
topology of the Fermi surface at low doping indicates a violation of
Luttinger's theorem. We discuss different ways of presenting the spectral data
to extract information about the Fermi surface. A comparison to recent
experiments will be presented.Comment: 8 pages, 7 color figures, uses RevTeX
Dynamical Cluster Approximation Employing FLEX as a Cluster Solver
We employ the Dynamical Cluster Approximation (DCA) in conjunction with the
Fluctuation Exchange Approximation (FLEX) to study the Hubbard model. The DCA
is a technique to systematically restore the momentum conservation at the
internal vertices of Feynman diagrams relinquished in the Dynamical Mean Field
Approximation (DMFA). FLEX is a perturbative diagrammatic approach in which
classes of Feynman diagrams are summed over analytically using geometric
series. The FLEX is used as a tool to investigate the complementarity of the
DCA and the finite size lattice technique with periodic boundary conditions by
comparing their results for the Hubbard model. We also study the microscopic
theory underlying the DCA in terms of compact (skeletal) and non-compact
diagrammatic contributions to the thermodynamic potential independent of a
specific model. The significant advantages of the DCA implementation in
momentum space suggests the development of the same formalism for the frequency
space. However, we show that such a formalism for the Matsubara frequencies at
finite temperatures leads to acausal results and is not viable. However, a real
frequency approach is shown to be feasible.Comment: 15 pages, 24 figures. Submitted to Physical Review B as a Regular
Articl
The boson-fermion model with on-site Coulomb repulsion between fermions
The boson-fermion model, describing a mixture of itinerant electrons
hybridizing with tightly bound electron pairs represented as hard-core bosons,
is here generalized with the inclusion of a term describing on-site Coulomb
repulsion between fermions with opposite spins. Within the general framework of
the Dynamical Mean-Field Theory, it is shown that around the symmetric limit of
the model this interaction strongly competes with the local boson-fermion
exchange mechanism, smoothly driving the system from a pseudogap phase with
poor conducting properties to a metallic regime characterized by a substantial
reduction of the fermionic density. On the other hand, if one starts from
correlated fermions described in terms of the one-band Hubbard model, the
introduction in the half-filled insulating phase of a coupling with hard-core
bosons leads to the disappearance of the correlation gap, with a consequent
smooth crossover to a metallic state.Comment: 7 pages, 6 included figures, to appear in Phys. Rev.
A Quantum Monte Carlo algorithm for non-local corrections to the Dynamical Mean-Field Approximation
We present the algorithmic details of the dynamical cluster approximation
(DCA), with a quantum Monte Carlo (QMC) method used to solve the effective
cluster problem. The DCA is a fully-causal approach which systematically
restores non-local correlations to the dynamical mean field approximation
(DMFA) while preserving the lattice symmetries. The DCA becomes exact for an
infinite cluster size, while reducing to the DMFA for a cluster size of unity.
We present a generalization of the Hirsch-Fye QMC algorithm for the solution of
the embedded cluster problem. We use the two-dimensional Hubbard model to
illustrate the performance of the DCA technique. At half-filling, we show that
the DCA drives the spurious finite-temperature antiferromagnetic transition
found in the DMFA slowly towards zero temperature as the cluster size
increases, in conformity with the Mermin-Wagner theorem. Moreover, we find that
there is a finite temperature metal to insulator transition which persists into
the weak-coupling regime. This suggests that the magnetism of the model is
Heisenberg like for all non-zero interactions. Away from half-filling, we find
that the sign problem that arises in QMC simulations is significantly less
severe in the context of DCA. Hence, we were able to obtain good statistics for
small clusters. For these clusters, the DCA results show evidence of non-Fermi
liquid behavior and superconductivity near half-filling.Comment: 25 pages, 15 figure
Spectral functions in itinerant electron systems with geometrical frustration
The Hubbard model with geometrical frustration is investigated in a metallic
phase close to half-filling. We calculate the single particle spectral function
for the triangular lattice within dynamical cluster approximation, which is
further combined with non-crossing approximation and fluctuation exchange
approximation to treat the resulting cluster Anderson model. It is shown that
frustration due to non-local correlations suppresses short-range
antiferromagnetic fluctuations and thereby assists the formation of heavy
quasi-particles near half-filling.Comment: 4 pages, 5 eps figure
Functional renormalization group approach to zero-dimensional interacting systems
We apply the functional renormalization group method to the calculation of
dynamical properties of zero-dimensional interacting quantum systems. As case
studies we discuss the anharmonic oscillator and the single impurity Anderson
model. We truncate the hierarchy of flow equations such that the results are at
least correct up to second order perturbation theory in the coupling. For the
anharmonic oscillator energies and spectra obtained within two different
functional renormalization group schemes are compared to numerically exact
results, perturbation theory, and the mean field approximation. Even at large
coupling the results obtained using the functional renormalization group agree
quite well with the numerical exact solution. The better of the two schemes is
used to calculate spectra of the single impurity Anderson model, which then are
compared to the results of perturbation theory and the numerical
renormalization group. For small to intermediate couplings the functional
renormalization group gives results which are close to the ones obtained using
the very accurate numerical renormalization group method. In particulare the
low-energy scale (Kondo temperature) extracted from the functional
renormalization group results shows the expected behavior.Comment: 22 pages, 8 figures include