842 research outputs found
Luttinger liquids with boundaries: Power-laws and energy scales
We present a study of the one-particle spectral properties for a variety of
models of Luttinger liquids with open boundaries. We first consider the
Tomonaga-Luttinger model using bosonization. For weak interactions the boundary
exponent of the power-law suppression of the spectral weight close to the
chemical potential is dominated by a term linear in the interaction. This
motivates us to study the spectral properties also within the Hartree-Fock
approximation. It already gives power-law behavior and qualitative agreement
with the exact spectral function. For the lattice model of spinless fermions
and the Hubbard model we present numerically exact results obtained using the
density-matrix renormalization-group algorithm. We show that many aspects of
the behavior of the spectral function close to the boundary can again be
understood within the Hartree-Fock approximation. For the repulsive Hubbard
model with interaction U the spectral weight is enhanced in a large energy
range around the chemical potential. At smaller energies a power-law
suppression, as predicted by bosonization, sets in. We present an analytical
discussion of the crossover and show that for small U it occurs at energies
exponentially (in -1/U) close to the chemical potential, i.e. that bosonization
only holds on exponentially small energy scales. We show that such a crossover
can also be found in other models.Comment: 16 pages, 9 figures included, submitted for publicatio
Resonant electronic Raman scattering near a quantum critical point
We calculate the resonant electronic Raman scattering for the Falicov-Kimball
model near the Mott transition on a hypercubic lattice. The solution is exact,
and employs dynamical mean field theory.Comment: 2 pages, 2 figures, contribution to the SCES04 conferenc
Optimization of Gutzwiller Wavefunctions in Quantum Monte Carlo
Gutzwiller functions are popular variational wavefunctions for correlated
electrons in Hubbard models. Following the variational principle, we are
interested in the Gutzwiller parameters that minimize e.g. the expectation
value of the energy. Rewriting the expectation value as a rational function in
the Gutzwiller parameters, we find a very efficient way for performing that
minimization. The method can be used to optimize general Gutzwiller-type
wavefunctions both, in variational and in fixed-node diffusion Monte Carlo.Comment: 9 pages RevTeX with 10 eps figure
Resonant Enhancement of Electronic Raman Scattering
We present an exact solution for electronic Raman scattering in a
single-band, strongly correlated material, including nonresonant, resonant and
mixed contributions. Results are derived for the spinless Falicov-Kimball
model, employing dynamical mean field theory; this system can be tuned through
a Mott metal-insulator transition.Comment: 4 pages, 3 figures, contribution to the SNS'2004 conferenc
Generalized Numerical Renormalization Group for Dynamical Quantities
In this paper we introduce a new approach for calculating dynamical
properties within the numerical renormalization group. It is demonstrated that
the method previously used fails for the Anderson impurity in a magnetic field
due to the absence of energy scale separation. The problem is solved by
evaluating the Green function with respect to the reduced density matrix of the
full system, leading to accurate spectra in agreement with the static
magnetization. The new procedure (denoted as DM-NRG) provides a unifying
framework for calculating dynamics at any temperature and represents the
correct extension of Wilson's original thermodynamic calculation.Comment: 4 pages RevTeX, 6 eps figures include
Spatial Correlations in Dynamical Mean Field Theory
We further develop an extended dynamical mean field approach introduced
earlier. It goes beyond the standard dynamical mean field theory by
incorporating quantum fluctuations associated with intersite (RKKY-like)
interactions. This is achieved by scaling the intersite interactions to the
same power in 1/D as that for the kinetic terms. In this approach, a correlated
lattice problem is reduced to a single-impurity Anderson model with additional
self-consistent bosonic baths. Here, we formulate the approach in terms of
perturbation expansions. We show that the two-particle vertex functions are
momentum-dependent, while the single-particle self-energy remains local. In
spite of this, the approach is conserving. Finally, we also determine the form
of a momentum-dependent dynamical susceptibility; the resulting expression
relates it to the corresponding Weiss field, local correlation function and
(momentum-dependent) intersite coupling.Comment: 28 pages, REVTEX, 8 figures include
Asymptotically exact mean field theory for the Anderson model including double occupancy
The Anderson impurity model for finite values of the Coulomb repulsion is
studied using a slave boson representation for the empty and doubly occupied
-level. In order to avoid well known problems with a naive mean field theory
for the boson fields, we use the coherent state path integral representation to
first integrate out the double occupancy slave bosons. The resulting effective
action is linearized using {\bf two-time} auxiliary fields. After integration
over the fermionic degrees of freedom one obtains an effective action suitable
for a -expansion. Concerning the constraint the same problem remains as
in the infinite case. For and
exact results for the ground state properties are recovered in the saddle point
approximation. Numerical solutions of the saddle point equations show that even
in the spindegenerate case the results are quite good.Comment: 19, RevTeX, cond-mat/930502
Boundary effects on one-particle spectra of Luttinger liquids
We calculate one-particle spectra for a variety of models of Luttinger
liquids with open boundary conditions. For the repulsive Hubbard model the
spectral weight close to the boundary is enhanced in a large energy range
around the chemical potential. A power law suppression, previously predicted by
bosonization, only occurs after a crossover at energies very close to the
chemical potential. Our comparison with exact spectra shows that the effects of
boundaries can partly be understood within the Hartree-Fock approximation.Comment: 4 pages including 4 figures, revised version, to be published in
Phys. Rev. B, January 200
Strong-Coupling Expansion for the Hubbard Model
A strong-coupling expansion for models of correlated electrons in any
dimension is presented. The method is applied to the Hubbard model in
dimensions and compared with numerical results in . Third order expansion
of the Green function suffices to exhibit both the Mott metal-insulator
transition and a low-temperature regime where antiferromagnetic correlations
are strong. It is predicted that some of the weak photoemission signals
observed in one-dimensional systems such as should become stronger as
temperature increases away from the spin-charge separated state.Comment: 4 pages, RevTex, 3 epsf figures include
Dynamics of disordered heavy Fermion systems
Dynamics of the disordered heavy Fermion model of Dobrosavljevic et al. are
calculated using an expression for the spectral function of the Anderson model
which is consistent with quantum Monte Carlo results. We compute the
self-energy for three distributions of Kondo scales including the distribution
of Bernal et al. for UCu{5-x}Pd{x}. The corresponding low temperature optical
conductivity shows a low-frequency pseudogap, a negative optical mass
enhancement, and a linear in frequency transport scattering rate, consistent
with results in Y{1-x}U{x}Pd{3} and UCu{5-x}Pd{x}.Comment: 5 pages, LaTeX and 4 PS figure
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