1,412 research outputs found
From infinite to two dimensions through the functional renormalization group
We present a novel scheme for an unbiased and non-perturbative treatment of
strongly correlated fermions. The proposed approach combines two of the most
successful many-body methods, i.e., the dynamical mean field theory (DMFT) and
the functional renormalization group (fRG). Physically, this allows for a
systematic inclusion of non-local correlations via the flow equations of the
fRG, after the local correlations are taken into account non-perturbatively by
the DMFT. To demonstrate the feasibility of the approach, we present numerical
results for the two-dimensional Hubbard model at half-filling.Comment: 5 pages, 4 figure
Exact analytic results for the Gutzwiller wave function with finite magnetization
We present analytic results for ground-state properties of Hubbard-type
models in terms of the Gutzwiller variational wave function with non-zero
values of the magnetization m. In dimension D=1 approximation-free evaluations
are made possible by appropriate canonical transformations and an analysis of
Umklapp processes. We calculate the double occupation and the momentum
distribution, as well as its discontinuity at the Fermi surface, for arbitrary
values of the interaction parameter g, density n, and magnetization m. These
quantities determine the expectation value of the one-dimensional Hubbard
Hamiltonian for any symmetric, monotonically increasing dispersion epsilon_k.
In particular for nearest-neighbor hopping and densities away from half filling
the Gutzwiller wave function is found to predict ferromagnetic behavior for
sufficiently large interaction U.Comment: REVTeX 4, 32 pages, 8 figure
Quantum phase transitions and collapse of the Mott gap in the dimensional half-filled Hubbard model
We study the low-energy asymptotics of the half-filled Hubbard model with a
circular Fermi surface in continuous dimensions, based on the
one-loop renormalization-group (RG) method. Peculiarity of the
dimensions is incorporated through the mathematica structure of the elementary
particle-partcile (PP) and particle-hole (PH) loops: infrared logarithmic
singularity of the PH loop is smeared for . The RG flows indicate
that a quantum phase transition (QPT) from a metallic phase to the Mott
insulator phase occurs at a finite on-site Coulomb repulsion for
. We also discuss effects of randomness.Comment: 12 pages, 10 eps figure
The anharmonic electron-phonon problem
The anharmonic electron-phonon problem is solved in the infinite-dimensional
limit using quantum Monte Carlo simulation. Charge-density-wave order is seen
to remain at half filling even though the anharmonicity removes the
particle-hole symmetry (and hence the nesting instability) of the model.
Superconductivity is strongly favored away from half filling (relative to the
charge-density-wave order) but the anharmonicity does not enhance transition
temperatures over the maximal values found in the harmonic limit.Comment: 5 pages typeset in ReVTeX. Four encapsulated postscript files
include
Hole dynamics in generalized spin backgrounds in infinite dimensions
We calculate the dynamical behaviour of a hole in various spin backgrounds in
infinite dimensions, where it can be determined exactly. We consider hypercubic
lattices with two different types of spin backgrounds. On one hand we study an
ensemble of spin configurations with an arbitrary spin probability on each
sublattice. This model corresponds to a thermal average over all spin
configurations in the presence of staggered or uniform magnetic fields. On the
other hand we consider a definite spin state characterized by the angle between
the spins on different sublattices, i.e a classical spin system in an external
magnetic field. When spin fluctuations are considered, this model describes the
physics of unpaired particles in strong coupling superconductors.Comment: Accepted in Phys. Rev. B. 18 pages of text (1 fig. included) in Latex
+ 2 figures in uuencoded form containing the 2 postscripts (mailed
separately
Competition between electron-phonon attraction and weak Coulomb repulsion
The Holstein-Hubbard model is examined in the limit of infinite dimensions.
Conventional folklore states that charge-density-wave (CDW) order is more
strongly affected by Coulomb repulsion than superconducting order because of
the pseudopotential effect. We find that both incommensurate CDW and
superconducting phases are stabilized by the Coulomb repulsion, but,
surprisingly, the commensurate CDW transition temperature is more robust than
the superconducting transition temperature. This puzzling feature is resolved
by a detailed analysis of perturbation theory.Comment: 13 pages in ReVTex including 3 encapsulated postscript files
(embedded in the text). The encapsulated postscript files are compressed and
uuencoded after the TeX file
Vertex-corrected perturbation theory for the electron-phonon problem with non-constant density of states
A series of weak-coupling perturbation theories which include the
lowest-order vertex corrections are applied to the attractive Holstein model in
infinite dimensions. The approximations are chosen to reproduce the iterated
perturbation theory in the limit of half-filling and large phonon frequency
(where the Holstein model maps onto the Hubbard model). Comparison is made with
quantum Monte Carlo solutions to test the accuracy of different approximation
schemes.Comment: 31 pages, 15 figures, typeset in ReVTe
Inhomogeneous Gutzwiller approximation with random phase fluctuations for the Hubbard model
We present a detailed study of the time-dependent Gutzwiller approximation
for the Hubbard model. The formalism, labelled GA+RPA, allows us to compute
random-phase approximation-like (RPA) fluctuations on top of the Gutzwiller
approximation (GA). No restrictions are imposed on the charge and spin
configurations which makes the method suitable for the calculation of linear
excitations around symmetry-broken solutions. Well-behaved sum rules are obeyed
as in the Hartree-Fock (HF) plus RPA approach. Analytical results for a
two-site model and numerical results for charge-charge and current-current
dynamical correlation functions in one and two dimensions are compared with
exact and HF+RPA results, supporting the much better performance of GA+RPA with
respect to conventional HF+RPA theory.Comment: 14 pages, 6 figure
The zero-dimensional O(N) vector model as a benchmark for perturbation theory, the large-N expansion and the functional renormalization group
We consider the zero-dimensional O(N) vector model as a simple example to
calculate n-point correlation functions using perturbation theory, the large-N
expansion, and the functional renormalization group (FRG). Comparing our
findings with exact results, we show that perturbation theory breaks down for
moderate interactions for all N, as one should expect. While the
interaction-induced shift of the free energy and the self-energy are well
described by the large-N expansion even for small N, this is not the case for
higher-order correlation functions. However, using the FRG in its one-particle
irreducible formalism, we see that very few running couplings suffice to get
accurate results for arbitrary N in the strong coupling regime, outperforming
the large-N expansion for small N. We further remark on how the derivative
expansion, a well-known approximation strategy for the FRG, reduces to an exact
method for the zero-dimensional O(N) vector model.Comment: 13 pages, 13 figure
Slave-Boson Functional-Integral Approach to the Hubbard Model with Orbital Degeneracy
A slave-boson functional-integral method has been developed for the Hubbard
model with arbitrary, orbital degeneracy . Its saddle-point mean-field
theory is equivalent to the Gutzwiller approximation, as in the case of
single-band Hubbard model. Our theory is applied to the doubly degenerate () model, and numerical calculations have been performed for this model in the
paramagnetic states. The effect of the exchange interaction on the
metal-insulator (MI) transition is discussed. The critical interaction for the
MI transition is analytically calculated as functions of orbital degeneracy and
electron occupancy.Comment: Latex 20 pages, 9 figures available on request to
[email protected] Note: published in J. Physical Society of Japan with
some minor modification
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