16 research outputs found
Bose-Hubbard model with random impurities: Multiband and nonlinear hopping effects
We investigate the phase diagrams of theoretical models describing bosonic
atoms in a lattice in the presence of randomly localized impurities. By
including multiband and nonlinear hopping effects we enrich the standard model
containing only the chemical-potential disorder with the site-dependent hopping
term. We compare the extension of the MI and the BG phase in both models using
a combination of the local mean-field method and a Hartree-Fock-like procedure,
as well as, the Gutzwiller-ansatz approach. We show analytical argument for the
presence of triple points in the phase diagram of the model with
chemical-potential disorder. These triple points however, cease to exists after
the addition of the hopping disorder.Comment: version accepted in Phys. Rev.
Long-range multipartite entanglement close to a first order quantum phase transition
We provide insight in the quantum correlations structure present in strongly
correlated systems beyond the standard framework of bipartite entanglement. To
this aim we first exploit rotationally invariant states as a test bed to detect
genuine tripartite entanglement beyond the nearest-neighbor in spin-1/2 models.
Then we construct in a closed analytical form a family of entanglement
witnesses which provides a sufficient condition to determine if a state of a
many-body system formed by an arbitrary number of spin-1/2 particles possesses
genuine tripartite entanglement, independently of the details of the model. We
illustrate our method by analyzing in detail the anisotropic XXZ spin chain
close to its phase transitions, where we demonstrate the presence of long range
multipartite entanglement near the critical point and the breaking of the
symmetries associated to the quantum phase transition.Comment: 6 pages, 3 figures, RevTeX 4, the abstract was changed and the
manuscript was extended including the contents of the previous appendix
Beyond the standard entropic inequalities: stronger scalar separability criteria and their applications
Recently it was shown that if a given state fulfils the reduction criterion
it must also satisfy the known entropic inequalities. Now the questions arises
whether on the assumption that stronger criteria based on positive but not
completely positive maps are satisfied, it is possible to derive some scalar
inequalities stronger than the entropic ones. In this paper we show that under
some assumptions the extended reduction criterion [H.-P. Breuer, Phys. Rev.
Lett 97, 080501 (2006); W. Hall, J. Phys. A 40, 6183 (2007)] leads to some
entropic--like inequalities which are much stronger than their entropic
counterparts. The comparison of the derived inequalities with other
separability criteria shows that such approach might lead to strong scalar
criteria detecting both distillable and bound entanglement. In particular, in
the case of SO(3)-invariant states it is shown that the present inequalities
detect entanglement in regions in which entanglement witnesses based on
extended reduction map fail. It should be also emphasized that in the case of
states the derived inequalities detect entanglement efficiently,
while the extended reduction maps are useless when acting on the qubit
subsystem. Moreover, there is a natural way to construct a many-copy
entanglement witnesses based on the derived inequalities so, in principle,
there is a possibility of experimental realization. Some open problems and
possibilities for further studies are outlined.Comment: 15 Pages, RevTex, 7 figures, some new results were added, few
references changed, typos correcte
Convergence of expansions in Schr\"odinger and Dirac eigenfunctions, with an application to the R-matrix theory
Expansion of a wave function in a basis of eigenfunctions of a differential
eigenvalue problem lies at the heart of the R-matrix methods for both the
Schr\"odinger and Dirac particles. A central issue that should be carefully
analyzed when functional series are applied is their convergence. In the
present paper, we study the properties of the eigenfunction expansions
appearing in nonrelativistic and relativistic -matrix theories. In
particular, we confirm the findings of Rosenthal [J. Phys. G: Nucl. Phys. 13,
491 (1987)] and Szmytkowski and Hinze [J. Phys. B: At. Mol. Opt. Phys. 29, 761
(1996); J. Phys. A: Math. Gen. 29, 6125 (1996)] that in the most popular
formulation of the R-matrix theory for Dirac particles, the functional series
fails to converge to a claimed limit.Comment: Revised version, accepted for publication in Journal of Mathematical
Physics, 21 pages, 1 figur
Rotationally invariant bipartite states and bound entanglement
We consider rotationally invariant states in \mathbb{C}^{N_{1}}\ot
\mathbb{C}^{N_{2}} Hilbert space with even and arbitrary
, and show that in such case there always exist states which
are inseparable and remain positive after partial transposition, and thus the
PPT criterion does not suffice to prove separability of such systems. We
demonstrate it applying a map developed recently by Breuer [H.-P. Breuer, Phys.
Rev. Lett {\bf 97}, 080501 (2006)] to states that remain invariant after
partial time reversal.Comment: 11 pages, 4 figures, accepted for publication in Physics Letters
A general scheme for construction of scalar separability criteria from positive maps
We present a general scheme that allows for construction of scalar
separability criteria from positive but not completely positive maps. The
concept is based on a decomposition of every positive map into a
difference of two completely positive maps , , i.e.,
. The scheme may be also treated as a
generalization of the known entropic inequalities, which are obtained from the
reduction map. An analysis performed on few classes of states shows that the
new scalar criteria are stronger than the entropic inequalities and
furthermore, when derived from indecomposable maps allow for detection of bound
entanglement.Comment: RevTex, 5 pages, 2 figures, the revised versio
Beyond pure state entanglement for atomic ensembles
We analyze multipartite entanglement between atomic ensembles within quantum
matter-light interfaces. In our proposal, a polarized light beam crosses
sequentially several polarized atomic ensembles impinging on each of them at a
given angle \alpha_i. These angles are crucial parameters for shaping the
entanglement since they are directly connected to the appropriate combinations
of the collective atomic spins that are squeezed. We exploit such scheme to go
beyond the pure state paradigm proposing realistic experimental settings to
address multipartite mixed state entanglement in continuous variables.Comment: 23 pages, 5 figure
Hidden string order in a hole superconductor with extended correlated hopping
Ultracold fermions in one-dimensional, spin-dependent nonoverlapping optical lattices are described by a nonstandard Hubbard model with next-nearest-neighbor correlated hopping. In the limit of a kinetically constraining value of the correlated hopping equal to the normal hopping, we map the invariant subspaces of the Hamiltonian exactly to free spinless fermion chains of varying lengths. As a result, the system exactly manifests spin-charge separation and we obtain the system properties for arbitrary filling: ground state collective order characterized by a spin gap, which can be ascribed to an unconventional critical hole superconductor associated with finite long range nonlocal string order. We study the system numerically away from the integrable point and show the persistence of both long range string order and spin gap for appropriate parameters as well as a transition to a ferromagnetic state