356 research outputs found
Universal properties of hard-core bosons confined on one-dimensional lattices
Based on an exact treatment of hard-core bosons confined on one-dimensional
lattices, we obtain the large distance behavior of the one-particle density
matrix, and show how it determines the occupation of the lowest natural orbital
in the thermodynamic limit. We also study the occupation of
the natural orbitals for large- at low densities. Both quantities show
universal behavior independently of the confining potential. Finite-size
corrections and the momentum distribution function for finite systems are also
analyzed.Comment: Revtex file, 5 pages, 5 figures. Content and references added.
Published versio
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
Thermodynamics of the Antiferromagnetic Heisenberg Model on the Checkerboard Lattice
Employing numerical linked-cluster expansions (NLCEs) along with exact
diagonalizations of finite clusters with periodic boundary condition, we study
the energy, specific heat, entropy, and various susceptibilities of the
antiferromagnetic Heisenberg model on the checkerboard lattice. NLCEs, combined
with extrapolation techniques, allow us to access temperatures much lower than
those accessible to exact diagonalization and other series expansions. We find
that the high-temperature peak in specific heat decreases as the frustration
increases, consistent with the large amount of unquenched entropy in the region
around maximum classical frustration, where the nearest-neighbor and
next-nearest neighbor exchange interactions (J and J', respectively) have the
same strength, and with the formation of a second peak at lower temperatures.
The staggered susceptibility shows a change of character when J' increases
beyond 0.75J, implying the disappearance of the long-range antiferromagnetic
order at zero temperature. For J'=4J, in the limit of weakly coupled crossed
chains, we find large susceptibilities for stripe and Neel order with
Q=(pi/2,pi/2) at low temperatures with antiferromagnetic correlations along the
chains. Other magnetic and bond orderings, such as a plaquette valence-bond
solid and a crossed-dimer order suggested by previous studies, have also been
investigated.Comment: 10 pages, 13 figure
Superfluid to normal phase transition in strongly correlated bosons in two and three dimensions
Using quantum Monte Carlo simulations, we investigate the finite-temperature
phase diagram of hard-core bosons (XY model) in two- and three-dimensional
lattices. To determine the phase boundaries, we perform a finite-size-scaling
analysis of the condensate fraction and/or the superfluid stiffness. We then
discuss how these phase diagrams can be measured in experiments with trapped
ultracold gases, where the systems are inhomogeneous. For that, we introduce a
method based on the measurement of the zero-momentum occupation, which is
adequate for experiments dealing with both homogeneous and trapped systems, and
compare it with previously proposed approaches.Comment: 13 pages, 11 figures.
http://link.aps.org/doi/10.1103/PhysRevA.86.04362
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
Finite-temperature properties of hard-core bosons confined on one-dimensional optical lattices
We present an exact study of the finite-temperature properties of hard-core
bosons (HCB's) confined on one-dimensional optical lattices. Our solution of
the HCB problem is based on the Jordan-Wigner transformation and properties of
Slater determinants. We analyze the effects of the temperature on the behavior
of the one-particle correlations, the momentum distribution function, and the
lowest natural orbitals. In addition, we compare results obtained using the
grand-canonical and canonical descriptions for systems like the ones recently
achieved experimentally. We show that even for such small systems, as small as
10 HCB's in 50 lattice sites, there are only minor differences between the
energies and momentum distributions obtained within both ensembles.Comment: RevTex file, 12 pages, 16 figures, published versio
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
Short-Range Correlations and Cooling of Ultracold Fermions in the Honeycomb Lattice
We use determinantal quantum Monte Carlo simulations and numerical
linked-cluster expansions to study thermodynamic properties and short-range
spin correlations of fermions in the honeycomb lattice. We find that, at half
filling and finite temperatures, nearest-neighbor spin correlations can be
stronger in this lattice than in the square lattice, even in regimes where the
ground state in the former is a semimetal or a spin liquid. The honeycomb
lattice also exhibits a more pronounced anomalous region in the double
occupancy that leads to stronger adiabatic cooling than in the square lattice.
We discuss the implications of these findings for optical lattice experiments.Comment: 5 pages, 4 figure
Superfluid and Mott Insulator phases of one-dimensional Bose-Fermi mixtures
We study the ground state phases of Bose-Fermi mixtures in one-dimensional
optical lattices with quantum Monte Carlo simulations using the Canonical Worm
algorithm. Depending on the filling of bosons and fermions, and the on-site
intra- and inter-species interaction, different kinds of incompressible and
superfluid phases appear. On the compressible side, correlations between bosons
and fermions can lead to a distinctive behavior of the bosonic superfluid
density and the fermionic stiffness, as well as of the equal-time Green
functions, which allow one to identify regions where the two species exhibit
anticorrelated flow. We present here complete phase diagrams for these systems
at different fillings and as a function of the interaction parameters.Comment: 8 pages, 12 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
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