969 research outputs found
Size and shape of Mott regions for fermionic atoms in a two-dimensional optical lattice
We investigate the harmonic-trap control of size and shape of Mott regions in
the Fermi Hubbard model on a square optical lattice. The use of Lanczos
diagonalization on clusters with twisted boundary conditions, followed by an
average over 50-80 samples, drastically reduce finite-size effects in some
ground state properties; calculations in the grand canonical ensemble together
with a local-density approximation (LDA) allow us to simulate the radial
density distribution. We have found that as the trap closes, the atomic cloud
goes from a metallic state, to a Mott core, and to a Mott ring; the coverage of
Mott atoms reaches a maximum at the core-ring transition. A `phase diagram' in
terms of an effective density and the on-site repulsion is proposed, as a guide
to maximize the Mott coverage. We also predict that the usual experimentally
accessible quantities, the global compressibility and the average double
occupancy (rather, its density derivative) display detectable signatures of the
core-ring transition. Some spin correlation functions are also calculated, and
predict the existence N\'eel ordering within Mott cores and rings.Comment: 5 pages, 6 figure
Multiperiodic magnetic structures in Hubbard superlattices
We consider fermions in one-dimensional superlattices (SL's), modeled by
site-dependent Hubbard-U couplings arranged in a repeated pattern of repulsive
(i.e., U>0) and free (U=0) sites. Density Matrix Renormalization Group (DMRG)
diagonalization of finite systems is used to calculate the local moment and the
magnetic structure factor in the ground state. We have found four regimes for
magnetic behavior: uniform local moments forming a spin-density wave (SDW),
`floppy' local moments with short-ranged correlations, local moments on
repulsive sites forming long-period SDW's superimposed with short-ranged
correlations, and local moments on repulsive sites solely with long-period
SDW's; the boundaries between these regimes depend on the range of electronic
densities, rho, and on the SL aspect ratio. Above a critical electronic
density, rho_{uparrow downarrow}, the SDW period oscillates both with rho and
with the spacer thickness. The former oscillation allows one to reproduce all
SDW wave vectors within a small range of electronic densities, unlike the
homogeneous system. The latter oscillation is related to the exchange
oscillation observed in magnetic multilayers. A crossover between regimes of
`thin' to `thick' layers has also been observed.Comment: 9 two-column pages, 10 figure
Luttinger liquid superlattices: realization of gapless insulating phases
We investigate Luttinger Liquid superlattices, a periodic structure composed
of two kinds of one-dimensional systems of interacting electrons. We calculate
several properties of the low-energy sector: the effective charge and spin
velocities, the compressibility, various correlation functions, the Landauer
conductance and the Drude weight. The low-energy properties are subsumed into
effective parameters, much like homogeneous one-dimensional systems. A generic
result is the weighted average nature of these parameters, in proportion to the
spatial extent of the underlying subunits, pointing to the possibility of
``engineered'' structures. As a specific realization, we consider a
one-dimensional Hubbard superlattice, which consists of a periodic arrangement
of two long Hubbard chains with different coupling constants and different
hopping amplitudes. This system exhibits a rich phase diagram with several
phases, both metallic and insulating. We have found that gapless insulating
phases are present over a wide range of parameters.Comment: 16 pages, 15 figures, RevTeX
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