790 research outputs found
Optical excitations of Peierls-Mott insulators with bond disorder
The density-matrix renormalization group (DMRG) is employed to calculate
optical properties of the half-filled Hubbard model with nearest-neighbor
interactions. In order to model the optical excitations of oligoenes, a Peierls
dimerization is included whose strength for the single bonds may fluctuate.
Systems with up to 100 electrons are investigated, their wave functions are
analyzed, and relevant length-scales for the low-lying optical excitations are
identified. The presented approach provides a concise picture for the size
dependence of the optical absorption in oligoenes.Comment: 12 pages, 13 figures, submitted to Phys. Rev.
Strong-coupling approach to the Mott--Hubbard insulator on a Bethe lattice in Dynamical Mean-Field Theory
We calculate the Hubbard bands for the half-filled Hubbard model on a Bethe
lattice with infinite coordination number up to and including third order in
the inverse Hubbard interaction. We employ the Kato--Takahashi perturbation
theory to solve the self-consistency equation of the Dynamical Mean-Field
Theory analytically for the single-impurity Anderson model in multi-chain
geometry. The weight of the secondary Hubbard sub-bands is of fourth order so
that the two-chain geometry is sufficient for our study. Even close to the
Mott--Hubbard transition, our results for the Mott--Hubbard gap agree very well
with those from numerical Dynamical Density-Matrix Renormalization Group
(DDMRG) calculations. The density of states of the lower Hubbard band also
agrees very well with DDMRG data, apart from a resonance contribution at the
upper band edge which cannot be reproduced in low-order perturbation theory.Comment: 40 pages, 7 figure
Optical conductivity of the half-filled Hubbard chain
We combine well-controlled analytical and numerical methods to determine the
optical conductivity of the one-dimensional Mott-Hubbard insulator at zero
temperature. A dynamical density-matrix renormalization group method provides
the entire absorption spectrum for all but very small coupling strengths. In
this limit we calculate the conductivity analytically using exact
field-theoretical methods. Above the Lieb-Wu gap the conductivity exhibits a
characteristic square-root increase. For small to moderate interactions, a
sharp maximum occurs just above the gap. For larger interactions, another weak
feature becomes visible around the middle of the absorption band.Comment: 4 pages with 3 eps figures, published version (changes in text and
references
Response of Bose gases in time-dependent optical superlattices
The dynamic response of ultracold Bose gases in one-dimensional optical
lattices and superlattices is investigated based on exact numerical time
evolutions in the framework of the Bose-Hubbard model. The system is excited by
a temporal amplitude modulation of the lattice potential, as it was done in
recent experiments. For regular lattice potentials, the dynamic signatures of
the superfluid to Mott-insulator transition are studied and the position and
the fine-structure of the resonances is explained by a linear response
analysis. Using direct simulations and the perturbative analysis it is shown
that in the presence of a two-colour superlattice the excitation spectrum
changes significantly when going from the homogeneous Mott-insulator the quasi
Bose-glass phase. A characteristic and experimentally accessible signature for
the quasi Bose-glass is the appearance of low-lying resonances and a
suppression of the dominant resonance of the Mott-insulator phase.Comment: 20 pages, 9 figures; added references and corrected typo
Excitons in one-dimensional Mott insulators
We employ dynamical density-matrix renormalization group (DDMRG) and
field-theory methods to determine the frequency-dependent optical conductivity
in one-dimensional extended, half-filled Hubbard models. The field-theory
approach is applicable to the regime of `small' Mott gaps which is the most
difficult to access by DDMRG. For very large Mott gaps the DDMRG recovers
analytical results obtained previously by means of strong-coupling techniques.
We focus on exciton formation at energies below the onset of the absorption
continuum. As a consequence of spin-charge separation, these Mott-Hubbard
excitons are bound states of spinless, charged excitations (`holon-antiholon'
pairs). We also determine exciton binding energies and sizes. In contrast to
simple band insulators, we observe that excitons exist in the Mott-insulating
phase only for a sufficiently strong intersite Coulomb repulsion. Furthermore,
our results show that the exciton binding energy and size are not related in a
simple way to the strength of the Coulomb interaction.Comment: 15 pages, 6 eps figures, corrected typos in labels of figures 4,5,
and
Dispersive spectrum and orbital order of spinless p-band fermions in an optical lattice
We study single-particle properties of a spinless p-band correlated fermionic
gas in an optical lattice by means of a variational cluster approach (VCA). The
single-particle spectral function is almost flat at half-filling and develops a
strongly dispersive behavior at lower fillings. The competition between
different orbital orderings is studied as a function of filling. We observe
that an ``antiferromagnetic'' orbital order develops at half-filling and is
destroyed by doping the system evolving into a disordered orbital state. At low
filling limit, we discuss the possibility of ``ferromagnetic'' orbital order by
complementing the VCA result with observations based on a trial wave function.
We also study the behavior of the momentum distribution for different values of
the on-site interaction. Finally, we introduce an integration contour in the
complex plane which allows to efficiently carry out Matsubara-frequency sums.Comment: published versio
Bose-Fermi mixtures in 1D optical superlattices
The zero temperature phase diagram of binary boson-fermion mixtures in
two-colour superlattices is investigated. The eigenvalue problem associated
with the Bose-Fermi-Hubbard Hamiltonian is solved using an exact numerical
diagonalization technique, supplemented by an adaptive basis truncation scheme.
The physically motivated basis truncation allows to access larger systems in a
fully controlled and very flexible framework. Several experimentally relevant
observables, such as the matter-wave interference pattern and the
condensatefraction, are investigated in order to explore the rich phase
diagram. At symmetric half filling a phase similar to the Mott-insulating phase
in a commensurate purely bosonic system is identified and an analogy to recent
experiments is pointed out. Furthermore a phase of complete localization of the
bosonic species generated by the repulsive boson-fermion interaction is
identified. These localized condensates are of a different nature than the
genuine Bose-Einstein condensates in optical lattices.Comment: 18 pages, 9 figure
Dynamical density correlation function of 1D Mott insulators in a magnetic field
We consider the one dimensional (1D) extended Hubbard model at half filling
in the presence of a magnetic field. Using field theory techniques we calculate
the dynamical density-density correlation function in the
low-energy limit. When excitons are formed, a singularity appears in
at a particular energy and momentum transfer.Comment: 7 pages, 4 figure
Multi-band Gutzwiller wave functions for general on-site interactions
We introduce Gutzwiller wave functions for multi-band models with general
on-site Coulomb interactions. As these wave functions employ correlators for
the exact atomic eigenstates they are exact both in the non-interacting and in
the atomic limit. We evaluate them in infinite lattice dimensions for all
interaction strengths without any restrictions on the structure of the
Hamiltonian or the symmetry of the ground state. The results for the
ground-state energy allow us to derive an effective one-electron Hamiltonian
for Landau quasi-particles, applicable for finite temperatures and frequencies
within the Fermi-liquid regime. As applications for a two-band model we study
the Brinkman-Rice metal-to-insulator transition at half band-filling, and the
transition to itinerant ferromagnetism for two specific fillings, at and close
to a peak in the density of states of the non-interacting system. Our new
results significantly differ from those for earlier Gutzwiller wave functions
where only density-type interactions were included. When the correct spin
symmetries for the two-electron states are taken into account, the importance
of the Hund's-rule exchange interaction is even more pronounced and leads to
paramagnetic metallic ground states with large local magnetic moments.
Ferromagnetism requires fairly large interaction strengths, and the resulting
ferromagnetic state is a strongly correlated metal.Comment: 37 pages, 10 figures; accepted for publication in Phys. Rev. B 57
(March 15, 1998
Symmetry-projected variational approach for ground and excited states of the two-dimensional Hubbard model
We present a symmetry-projected configuration mixing scheme to describe
ground and excited states, with well defined quantum numbers, of the
two-dimensional Hubbard model with nearestneighbor hopping and periodic
boundary conditions. Results for the half-filled 2{\times}4, 4{\times}4, and
6{\times}6 lattices, as well as doped 4 {\times} 4 systems, compare well with
available results, both exact and from other state-of-the-art approximations.
We report spectral functions and density of states obtained from a
well-controlled ansatz for the (Ne {\pm} 1)-electron system. Symmetry projected
methods have been widely used for the many-body nuclear physics problem but
have received little attention in the solid state community. Given their
relatively low (mean-field) computational cost and the high quality of results
here reported, we believe that they deserve further scrutiny
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