416 research outputs found
Phase diagram of the hardcore Bose-Hubbard model on a checkerboard superlattice
We obtain the complete phase diagram of the hardcore Bose-Hubbard model in
the presence of a period-two superlattice in two and three dimensions. First we
acquire the phase boundaries between the superfluid phase and the `trivial'
insulating phases of the model (the completely-empty and completely-filled
lattices) analytically. Next, the boundary between the superfluid phase and the
half-filled Mott-insulating phase is obtained numerically, using the stochastic
series expansion (SSE) algorithm followed by finite-size scaling. We also
compare our numerical results against the predictions of several approximation
schemes, including two mean-field approaches and a fourth-order strong-coupling
expansion (SCE), where we show that the latter method in particular is
successful in producing an accurate picture of the phase diagram. Finally, we
examine the extent to which several approximation schemes, such as the random
phase approximation and the strong-coupling expansion, give an accurate
description of the momentum distribution of the bosons inside the insulating
phases.Comment: 11 pages, 7 figure
Supersolids in confined fermions on one-dimensional optical lattices
Using quantum Monte Carlo simulations, we show that density-density and
pairing correlation functions of the one-dimensional attractive fermionic
Hubbard model in a harmonic confinement potential are characterized by the
anomalous dimension of a corresponding periodic system, and hence
display quantum critical behavior. The corresponding fluctuations render the
SU(2) symmetry breaking by the confining potential irrelevant, leading to
structure form factors for both correlation functions that scale with the same
exponent upon increasing the system size, thus giving rise to a
(quasi)supersolid.Comment: 4 pages, 5 figures, published versio
Quantum quenches in disordered systems: Approach to thermal equilibrium without a typical relaxation time
We study spectral properties and the dynamics after a quench of
one-dimensional spinless fermions with short-range interactions and long-range
random hopping. We show that a sufficiently fast decay of the hopping term
promotes localization effects at finite temperature, which prevents
thermalization even if the classical motion is chaotic. For slower decays, we
find that thermalization does occur. However, within this model, the latter
regime falls in an unexpected universality class, namely, observables exhibit a
power-law (as opposed to an exponential) approach to their thermal expectation
values.Comment: 5 pages, 5 figure
Collective Oscillations of Strongly Correlated One-Dimensional Bosons on a Lattice
We study the dipole oscillations of strongly correlated 1D bosons, in the
hard-core limit, on a lattice, by an exact numerical approach. We show that far
from the regime where a Mott insulator appears in the system, damping is always
present and increases for larger initial displacements of the trap, causing
dramatic changes in the momentum distribution, . When a Mott insulator
sets in the middle of the trap, the center of mass barely moves after an
initial displacement, and remains very similar to the one in the ground
state. We also study changes introduced by the damping in the natural orbital
occupations, and the revival of the center of mass oscillations after long
times.Comment: 4 pages, 5 figures, published versio
Degenerate Fermi gas in a combined harmonic-lattice potential
In this paper we derive an analytic approximation to the density of states
for atoms in a combined optical lattice and harmonic trap potential as used in
current experiments with quantum degenerate gases. We compare this analytic
density of states to numerical solutions and demonstrate its validity regime.
Our work explicitly considers the role of higher bands and when they are
important in quantitative analysis of this system. Applying our density of
states to a degenerate Fermi gas we consider how adiabatic loading from a
harmonic trap into the combined harmonic-lattice potential affects the
degeneracy temperature. Our results suggest that occupation of excited bands
during loading should lead to more favourable conditions for realizing
degenerate Fermi gases in optical lattices.Comment: 11 pages, 9 figure
Free expansion of impenetrable bosons on one-dimensional optical lattices
We review recent exact results for the free expansion of impenetrable bosons
on one-dimensional lattices, after switching off a confining potential. When
the system is initially in a superfluid state, far from the regime in which the
Mott-insulator appears in the middle of the trap, the momentum distribution of
the expanding bosons rapidly approaches the momentum distribution of
noninteracting fermions. Remarkably, no loss in coherence is observed in the
system as reflected by a large occupation of the lowest eigenstate of the
one-particle density matrix. In the opposite limit, when the initial system is
a pure Mott insulator with one particle per lattice site, the expansion leads
to the emergence of quasicondensates at finite momentum. In this case,
one-particle correlations like the ones shown to be universal in the
equilibrium case develop in the system. We show that the out-of-equilibrium
behavior of the Shannon information entropy in momentum space, and its contrast
with the one of noninteracting fermions, allows to differentiate the two
different regimes of interest. It also helps in understanding the crossover
between them.Comment: 21 pages, 14 figures, invited brief revie
Time of flight observables and the formation of Mott domains of fermions and bosons on optical lattices
We study, using quantum Monte Carlo simulations, the energetics of the
formation of Mott domains of fermions and bosons trapped on one-dimensional
lattices. We show that, in both cases, the sum of kinetic and interaction
energies exhibits minima when Mott domains appear in the trap. In addition, we
examine the derivatives of the kinetic and interaction energies, and of their
sum, which display clear signatures of the Mott transition. We discuss the
relevance of these findings to time-of-flight experiments that could allow the
detection of the metal--Mott-insulator transition in confined fermions on
optical lattices, and support established results on the
superfluid--Mott-insulator transition in confined bosons on optical lattices.Comment: 5 pages, 6 figures, published versio
Coherent matter waves emerging from Mott-insulators
We study the formation of (quasi-)coherent matter waves emerging from a Mott
insulator for strongly interacting bosons on a one-dimensional lattice. It has
been shown previously that a quasi-condensate emerges at momentum k=\pi/2a,
where a is the lattice constant, in the limit of infinitely strong repulsion
(hard-core bosons). Here we show that this phenomenon persists for all values
of the repulsive interaction that lead to a Mott insulator at a commensurate
filling. The non-equilibrium dynamics of hard-core bosons is treated exactly by
means of a Jordan-Wigner transformation, and the generic case is studied using
a time-dependent density matrix renormalization group technique. Different
methods for controlling the emerging matter wave are discussed.Comment: 20 pages, 11 figures. Published versio
Exact coherent states of a harmonically confined Tonks-Girardeau gas
Using a scaling transformation we exactly determine the dynamics of an
harmonically confined Tonks-Girardeau gas under arbitrary time variations of
the trap frequency. We show how during a one-dimensional expansion a
``dynamical fermionization'' occurs as the momentum distribution rapidly
approaches an ideal Fermi gas distribution, and that under a sudden change of
the trap frequency the gas undergoes undamped breathing oscillations displaying
alternating bosonic and fermionic character in momentum space. The absence of
damping in the oscillations is a peculiarity of the truly Tonks regime.Comment: 4 pages, 2 figures, published versio
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