62 research outputs found
Ultracold atoms in one-dimensional optical lattices approaching the Tonks-Girardeau regime
Recent experiments on ultracold atomic alkali gases in a one-dimensional
optical lattice have demonstrated the transition from a gas of soft-core bosons
to a Tonks-Girardeau gas in the hard-core limit, where one-dimensional bosons
behave like fermions in many respects. We have studied the underlying many-body
physics through numerical simulations which accommodate both the soft-core and
hard-core limits in one single framework. We find that the Tonks-Girardeau gas
is reached only at the strongest optical lattice potentials. Results for
slightly higher densities, where the gas develops a Mott-like phase already at
weaker optical lattice potentials, show that these Mott-like short range
correlations do not enhance the convergence to the hard-core limit.Comment: 4 pages, 3 figures, replaced with published versio
Spin Stiffness in the Hubbard model
The spin stiffness of the repulsive Hubbard model that occurs
in the hydrodynamic theory of antiferromagnetic spin waves is shown to be the
same as the thermodynamically defined stiffness involved in twisting the order
parameter. New expressions for are derived, which enable easier
interpretation, and connections with superconducting weight and gauge
invariance are discussed.Comment: 21 Pages LaTeX2e, to be published in Journal of Physics
Particle-Hole Symmetry and the Effect of Disorder on the Mott-Hubbard Insulator
Recent experiments have emphasized that our understanding of the interplay of
electron correlations and randomness in solids is still incomplete. We address
this important issue and demonstrate that particle-hole (ph) symmetry plays a
crucial role in determining the effects of disorder on the transport and
thermodynamic properties of the half-filled Hubbard Hamiltonian. We show that
the low-temperature conductivity decreases with increasing disorder when
ph-symmetry is preserved, and shows the opposite behavior, i.e. conductivity
increases with increasing disorder, when ph-symmetry is broken. The Mott
insulating gap is insensitive to weak disorder when there is ph-symmetry,
whereas in its absence the gap diminishes with increasing disorder.Comment: 4 pages, 4 figure
Ising Expansion for the Hubbard Model
We develop series expansions for the ground state properties of the Hubbard
model, by introducing an Ising anisotropy into the Hamiltonian. For the
two-dimensional (2D) square lattice half-filled Hubbard model, the ground state
energy, local moment, sublattice magnetization, uniform magnetic susceptibility
and spin stiffness are calculated as a function of , where is the
Coulomb constant and is the hopping parameter. Magnetic susceptibility data
indicate a crossover around between spin density wave
antiferromagnetism and Heisenberg antiferromagnetism. Comparisons with Monte
Carlo simulations, RPA result and mean field solutions are also made.Comment: 22 pages, 6 Postscript figures, Revte
Superconductivity in the Hubbard model with correlated hopping: Slave-boson study
The slave boson mean-field studies of the ground state of the Hubbard model
with correlated hopping were performed. The approach qualitatively recovers the
exact results for the case of the hopping integral t equal to the correlated
hopping integral X. The phase diagram for the strongly correlated state with
only singly occupied sites, the weakly correlated state, where single and
double occupation is allowed, and for the superconducting state, was determined
for any values of X and any electron concentration n. At the half-filled band
(n=1) a direct transition from the superconductor to the Mott insulator was
found. In the region of strong correlations the superconducting solution is
stable for n close to 1, in contrast to the case of weak correlations, in which
superconductivity occurs at n close to 0 and n close to 2. We found also that
strong correlations change characteristics of the superconducting phase, e.g.
the gap in the excitation spectrum has a nonexponential dependence close to the
point of the phase transition.Comment: 13 pages, 24 Postscript figures (in 12 files
Short Range Interaction Effects on the Density of States of Disordered Two Dimensional Crystals with a half--filled band
The Density of electronic States (DoS) of a two--dimensional square lattice
with substitutional impurities is calculated in the presence of short--range
electron--electron interactions. In the middle of the energy band, the Bragg
reflections off the Brillouin zone boundary are shown to lead to additional
quantum corrections to the DoS, the sign of which is opposite to the sign of
the Altshuler--Aronov's logarithmic correction. The resulting quantum
correction to the DoS at half--filling is positive, i.e. the DoS increases
logarithmically as the Fermi energy is approached. However, far from the
commensurate points where the Bragg reflections are suppressed, the negative
logarithmic corrections to the DoS survive.Comment: 5 pages 2 figure
Delocalizing effect of the Hubbard repulsion for electrons on a two-dimensional disordered lattice
We study numerically the ground-state properties of the repulsive Hubbard
model for spin-1/2 electrons on two-dimensional lattices with disordered
on-site energies. The projector quantum Monte Carlo method is used to obtain
very accurate values of the ground-state charge density distributions with
and particles. The difference in these charge densities allows us
to study the localization properties of an added particle. The results obtained
at quarter-filling on finite clusters show that the Hubbard repulsion has a
strong delocalizing effect on the electrons in disordered 2D lattices. However,
numerical restrictions do not allow us to reach a definite conclusion about the
existence of a metal-insulator transition in the thermodynamic limit in
two-dimensions.Comment: revtex, 7 pages, 7 figure
Ground state properties of the 2D disordered Hubbard model
We study the ground state of the two-dimensional (2D) disordered Hubbard
model by means of the projector quantum Monte Carlo (PQMC) method. This
approach allows us to investigate the ground state properties of this model for
lattice sizes up to , at quarter filling, for a broad range of
interaction and disorder strengths. Our results show that the ground state of
this system of spin-1/2 fermions remains localised in the presence of the
short-ranged Hubbard interaction.Comment: 7 pages, 9 figure
Static overscreening and nonlinear response in the Hubbard Model
We investigate the static charge response for the Hubbard model. Using the
Slave-Boson method in the saddle-point approximation we calculate the charge
susceptibility. We find that RPA works quite well close to half-filling,
breaking, of course, down close to the Mott transition. Away from half filling
RPA is much less reliable: Already for very small values of the Hubbard
interaction U, the linear response becomes much more efficient than RPA,
eventually leading to overscreening already beyond quite moderate values of U.
To understand this behavior we give a simple argument, which implies that the
response to an external perturbation at large U should actually be strongly
non-linear. This prediction is confirmed by the results of exact
diagonalization.Comment: 10 pages, 7 figures, RevTe
Phase of bi-particle localized states for the Cooper problem in two-dimensional disordered systems
The Cooper problem is studied numerically for the Anderson model with
disorder in two-dimensions. It is shown that the attractive Hubbard interaction
creates a phase of bi-particle localized states in the regime where
non-interacting states are delocalized. This phase cannot be obtained in the
mean-field approximation and the pair coupling energy is strongly enhanced in
this regime. The effects of magnetic field are studied and it is shown that
under certain conditions they lead to delocalization.Comment: revtex, 7 pages, 8 figure
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