2,312 research outputs found
Multipartite Entanglement Signature of Quantum Phase Transitions
We derive a general relation between the non-analyticities of the ground
state energy and those of a subclass of the multipartite generalized global
entanglement (GGE) measure defined by T. R. de Oliveira et al. [Phys. Rev. A
73, 010305(R) (2006)] for many-particle systems. We show that GGE signals both
a critical point location and the order of a quantum phase transition (QPT). We
also show that GGE allows us to study the relation between multipartite
entanglement and QPTs, suggesting that multipartite but not bipartite
entanglement is favored at the critical point. Finally, using GGE we were able,
at a second order QPT, to define a diverging entanglement length (EL) in terms
of the usual correlation length. We exemplify this with the XY spin-1/2 chain
and show that the EL is half the correlation length.Comment: Published version. Incorporates correction made in erratu
Structural anomalies for a three dimensional isotropic core-softened potential
Using molecular dynamics simulations we investigate the structure of a system
of particles interacting through a continuous core-softened interparticle
potential. We found for the translational order parameter, t, a local maximum
at a density and a local minimum at . Between and , the parameter
anomalously decreases upon pressure. For the orientational order parameter,
, was observed a maximum at a density . For densities between and , both the
translational (t) and orientational () order parameters have anomalous
behavior. We know that this system also exhibits density and diffusion anomaly.
We found that the region in the pressure-temperature phase-diagram of the
structural anomaly englobes the region of the diffusion anomaly that is larger
than the region limited by the temperature of maximum density. This cascade of
anomalies (structural, dynamic and thermodynamic) for our model has the same
hierarchy of that one observed for the SPC/E water.Comment: 19 pages, 8 figure
Genuine Multipartite Entanglement in Quantum Phase Transitions
We demonstrate that the Global Entanglement (GE) measure defined by Meyer and
Wallach, J. Math. Phys. 43, 4273 (2002), is maximal at the critical point for
the Ising chain in a transverse magnetic field. Our analysis is based on the
equivalence of GE to the averaged linear entropy, allowing the understanding of
multipartite entanglement (ME) features through a generalization of GE for
bipartite blocks of qubits. Moreover, in contrast to GE, the proposed ME
measure can distinguish three paradigmatic entangled states: ,
, and . As such the generalized measure can detect
genuine ME and is maximal at the critical point.Comment: 4 pages, 3 figures. Replaced with final published versio
Multipartite Entanglement Signature Of Quantum Phase Transitions.
We derive a general relation between the nonanalyticities of the ground state energy and those of a subclass of the multipartite generalized global entanglement (GGE) measure defined by de Oliveira et al. [Phys. Rev. A 73, 010305(R) (2006)] for many-particle systems. We show that GGE signals both a critical point location and the order of a quantum phase transition (QPT). We also show that GGE allows us to study the relation between multipartite entanglement and QPTs, suggesting that multipartite but not bipartite entanglement is favored at the critical point. Finally, using GGE we were able, at a second-order QPT, to define a diverging entanglement length (EL) in terms of the usual correlation length. We exemplify this with the XY spin-1/2 chain and show that the EL is half the correlation length.9717040
Coherent state approach to the cross collisional effects in the population dynamics of a two-mode Bose-Einstein condensate
We reanalyze the non-linear population dynamics of a Bose-Einstein Condensate
(BEC) in a double well trap considering a semiclassical approach based on a
time dependent variational principle applied to coherent states associated to
SU(2) group. Employing a two-mode local approximation and hard sphere type
interaction, we show in the Schwinger's pseudo-spin language the occurrence of
a fixed point bifurcation that originates a separatrix of motion on a sphere.
This separatrix corresponds to the borderline between two dynamical regimes of
Josephson oscillations and mesoscopic self-trapping. We also consider the
effects of interaction between particles in different wells, known as cross
collisions. Such terms are usually neglected for traps sufficiently far apart,
but recently it has been shown that they contribute to the effective tunneling
constant with a factor growing linearly with the particle number. This effect
changes considerably the effective tunneling of the system for sufficiently
large number of trapped atoms, in perfect accord with experimental data.
Finally, we identify analytically the transition parameter associated to the
bifurcation in the generalized phase space of the model with cross-collision
terms, and show how the dynamical regime depends on the initial conditions of
the system and the collisional parameters values.Comment: 19 pages, 8 figures. Added some references, remarks on LMG model and
acknowledgment
Operational Classification and Quantification of Multipartite Entangled States
We formalize and extend an operational multipartite entanglement measure
introduced by T. R. Oliveira, G. Rigolin, and M. C. de Oliveira, Phys. Rev. A
73, 010305(R) (2006), through the generalization of global entanglement (GE)
[D. A. Meyer and N. R. Wallach, J. Math. Phys. 43, 4273 (2002)]. Contrarily to
GE the main feature of this measure lies in the fact that we study the mean
linear entropy of all possible partitions of a multipartite system. This allows
the construction of an operational multipartite entanglement measure which is
able to distinguish among different multipartite entangled states that GE
failed to discriminate. Furthermore, it is also maximum at the critical point
of the Ising chain in a transverse magnetic field, being thus able to detect a
quantum phase transition.Comment: 14 pages, RevTex4, published versio
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