2,573 research outputs found
Mott insulator to superfluid transition in the Bose-Hubbard model: a strong-coupling approach
We present a strong-coupling expansion of the Bose-Hubbard model which
describes both the superfluid and the Mott phases of ultracold bosonic atoms in
an optical lattice. By performing two successive Hubbard-Stratonovich
transformations of the intersite hopping term, we derive an effective action
which provides a suitable starting point to study the strong-coupling limit of
the Bose-Hubbard model. This action can be analyzed by taking into account
Gaussian fluctuations about the mean-field approximation as in the Bogoliubov
theory of the weakly interacting Bose gas. In the Mott phase, we reproduce
results of previous mean-field theories and also calculate the momentum
distribution function. In the superfluid phase, we find a gapless spectrum and
compare our results with the Bogoliubov theory.Comment: 8 pages, 6 figures; (v2) Two references adde
Quantum criticality of a Bose gas in an optical lattice near the Mott transition
We derive the equation of state of bosons in an optical lattice in the
framework of the Bose-Hubbard model. Near the density-driven Mott transition,
the expression of the pressure P({\mu},T) versus chemical potential and
temperature is similar to that of a dilute Bose gas but with renormalized mass
m^* and scattering length a^*. m^* is the mass of the elementary excitations at
the quantum critical point governing the transition from the superfluid phase
to the Mott insulating phase, while a^* is related to their effective
interaction at low energy. We use a nonperturbative renormalization-group
approach to compute these parameters as a function of the ratio t/U between
hopping amplitude and on-site repulsion.Comment: v1) 4 pages, 6 figures. v2) Significant rewriting (new title) with
more emphasis on the quantum critical behavior near the Mott transitio
Infrared behavior of interacting bosons at zero temperature
We review the infrared behavior of interacting bosons at zero temperature.
After a brief discussion of the Bogoliubov approximation and the breakdown of
perturbation theory due to infrared divergences, we present two approaches that
are free of infrared divergences -- Popov's hydrodynamic theory and the
non-perturbative renormalization group -- and allow us to obtain the exact
infrared behavior of the correlation functions. We also point out the
connection between the infrared behavior in the superfluid phase and the
critical behavior at the superfluid--Mott-insulator transition in the
Bose-Hubbard model.Comment: 8 pages, 4 figures. Proceedings of the 19th International Laser
Physics Workshop, LPHYS'10 (Foz do Iguacu, Brazil, July 5-9, 2010
A strong-coupling expansion for the Hubbard model
We reconsider the strong-coupling expansion for the Hubbard model recently
introduced by Sarker and Pairault {\it et al.} By introducing slave particles
that act as projection operators onto the empty, singly occupied and doubly
occupied atomic states, the perturbation theory around the atomic limit
distinguishes between processes that do conserve or do not conserve the total
number of doubly occupied sites. This allows for a systematic expansion
that does not break down at low temperature ( being the intersite hopping
amplitude and the local Coulomb repulsion). The fermionic field becomes a
two-component field, which reflects the presence of the two Hubbard bands. The
single-particle propagator is naturally expressed as a function of a matrix self-energy. Furthermore, by introducing a time- and
space-fluctuating spin-quantization axis in the functional integral, we can
expand around a ``non-degenerate'' ground-state where each singly occupied site
has a well defined spin direction (which may fluctuate in time). This formalism
is used to derive the effective action of charge carriers in the lower Hubbard
band to first order in . We recover the action of the t-J model in the
spin-hole coherent-state path integral. We also compare our results with those
previously obtained by studying fluctuations around the large- Hartree-Fock
saddle point.Comment: 20 pages RevTex, 3 figure
A Renormalization group approach for highly anisotropic 2D Fermion systems: application to coupled Hubbard chains
I apply a two-step density-matrix renormalization group method to the
anisotropic two-dimensional Hubbard model. As a prelude to this study, I
compare the numerical results to the exact one for the tight-binding model. I
find a ground-state energy which agrees with the exact value up to four digits
for systems as large as . I then apply the method to the
interacting case. I find that for strong Hubbard interaction, the ground-state
is dominated by magnetic correlations.
These correlations are robust even in the presence of strong frustration.
Interchain pair tunneling is negligible in the singlet and triplet channels and
it is not enhanced by frustration. For weak Hubbard couplings, interchain
non-local singlet pair tunneling is enhanced and magnetic correlations are
strongly reduced. This suggests a possible superconductive ground state.Comment: 8 pages, 11 figures, expanded version of cond-mat/060856
Weak Field Magnetoresistance in Quasi-One-Dimensional Systems
Theoretical studies are presented on weak localization effects and
magnetoresistance in quasi-one-dimensional systems with open Fermi surfaces.
Based on the Wigner representation, the magnetoresistance in the region of weak
field has been studied for five possible configurations of current and field
with respect to the one-dimensional axis. It has been indicated that the
anisotropy and its temperature dependences of the magnetoresistance will give
information on the degree of one-dimensionality and the phase relaxation time.Comment: pages 11, LaTeX, 5 figures, uses jpsj.sty. To be published in J.
Phys. Soc. Jpn. (Vol.67(1998) No.4); Added some references and a Note at Feb.
13 199
Collective modes in a system with two spin-density waves: the `Ribault' phase of quasi-one-dimensional organic conductors
We study the long-wavelength collective modes in the magnetic-field-induced
spin-density-wave (FISDW) phases experimentally observed in organic conductors
of the Bechgaard salts family, focusing on phases that exhibit a sign reversal
of the quantum Hall effect (Ribault anomaly). We have recently proposed that
two SDW's coexist in the Ribault phase, as a result of Umklapp processes. When
the latter are strong enough, the two SDW's become circularly polarized
(helicoidal SDW's). In this paper, we study the collective modes which result
from the presence of two SDW's. We find two Goldstone modes, an out-of-phase
sliding mode and an in-phase spin-wave mode, and two gapped modes. The sliding
Goldstone mode carries only a fraction of the total optical spectral weight,
which is determined by the ratio of the amplitude of the two SDW's. In the
helicoidal phase, all the spectral weight is pushed up above the SDW gap. We
also point out similarities with phase modes in two-band or bilayer
superconductors. We expect our conclusions to hold for generic two-SDW systems.Comment: Revised version, 25 pages, RevTex, 7 figure
Superconductivity of Quasi-One and Quasi-Two Dimensional Tight-Binding Electrons in Magnetic Field
The upper critical field of the tight-binding electrons in the
three-dimensional lattice is investigated.
The electrons make Cooper pairs between the eigenstates with the same energy
in the strong magnetic field. The transition lines in the quasi-one dimensional
case are shown to deviate from the previously obtained results where the
hopping matrix elements along the magnetic field are neglected. In the absence
of the Pauli pair breaking the transition temperature of the quasi-two
dimensional electrons is obtained to oscillationally increase as the magnetic
field becomes large and reaches to in the strong field as in the
quasi-one dimensional case.Comment: 4pages,4figures,to be published in J.Phys.Soc.Jp
Mixture of Kernels and Iterated Semidirect Product of Diffeomorphisms Groups
In the framework of large deformation diffeomorphic metric mapping (LDDMM),
we develop a multi-scale theory for the diffeomorphism group based on previous
works. The purpose of the paper is (1) to develop in details a variational
approach for multi-scale analysis of diffeomorphisms, (2) to generalise to
several scales the semidirect product representation and (3) to illustrate the
resulting diffeomorphic decomposition on synthetic and real images. We also
show that the approaches presented in other papers and the mixture of kernels
are equivalent.Comment: 21 pages, revised version without section on evaluatio
Berezinskii-Kosterlitz-Thouless transition and BCS-Bose crossover in the two-dimensional attractive Hubbard model
We study the two-dimensional attractive Hubbard model using the mapping onto
the half-filled repulsive Hubbard model in a uniform magnetic field coupled to
the fermion spins. The low-energy effective action for charge and pairing
fluctuations is obtained in the hydrodynamic regime. We recover the action of a
Bose superfluid where half the fermion density is identified as the conjugate
variable of the phase of the superconducting order parameter. By integrating
out charge fluctuations, we obtain a phase-only action. In the zero-temperature
superconducting state, this action describes a collective phase mode smoothly
evolving from the Anderson-Bogoliubov mode at weak coupling to the Bogoliubov
mode of a Bose superfluid at strong coupling. At finite temperature, the
phase-only action can be used to extract an effective XY model and thus obtain
the Berezinskii-Kosterlitz-Thouless (BKT) phase transition temperature. We also
identify a renormalized classical regime of superconducting fluctuations above
the BKT phase transition, and a regime of incoherent pairs at higher
temperature. Special care is devoted to the nearly half-filled case where the
symmetry of the order parameter is enlarged to SO(3) due to strong charge fluctuations. The low-energy effective action is then an
SO(3) non-linear sigma model with a (symmetry breaking) magnetic field
proportional to the doping. In the strong-coupling limit, the attractive
Hubbard model can be mapped onto the Heisenberg model, from which we recover
the Gross-Pitaevskii equation in the low-density limit.Comment: 31 pages, 12 figures, RevTex4; (v2) changes following referees'
comments, references adde
- …