9 research outputs found
Thermal and ground-state entanglement in Heisenberg XX qubit rings
We study the entanglement of thermal and ground states in Heisernberg
qubit rings with a magnetic field. A general result is found that for
even-number rings pairwise entanglement between nearest-neighbor qubits is
independent on both the sign of exchange interaction constants and the sign of
magnetic fields. As an example we study the entanglement in the four-qubit
model and find that the ground state of this model without magnetic fields is
shown to be a four-body maximally entangled state measured by the -tangle.Comment: Four pages and one figure, small change
Entanglement in SU(2)-invariant quantum spin systems
We analyze the entanglement of SU(2)-invariant density matrices of two spins
, using the Peres-Horodecki criterion. Such density
matrices arise from thermal equilibrium states of isotropic spin systems. The
partial transpose of such a state has the same multiplet structure and
degeneracies as the original matrix with eigenvalue of largest multiplicity
being non-negative. The case , can be solved completely
and is discussed in detail with respect to isotropic Heisenberg spin models.
Moreover, in this case the Peres-Horodecki ciriterion turns out to be a
sufficient condition for non-separability. We also characterize SU(2)-invariant
states of two spins of length 1.Comment: 5 page
Various correlations in a Heisenberg XXZ spin chain both in thermal equilibrium and under the intrinsic decoherence
In this paper we discuss various correlations measured by the concurrence
(C), classical correlation (CC), quantum discord (QD), and geometric measure of
discord (GMD) in a two-qubit Heisenberg XXZ spin chain in the presence of
external magnetic field and Dzyaloshinskii-Moriya (DM) anisotropic
antisymmetric interaction. Based on the analytically derived expressions for
the correlations for the cases of thermal equilibrium and the inclusion of
intrinsic decoherence, we discuss and compare the effects of various system
parameters on the correlations in different cases. The results show that the
anisotropy Jz is considerably crucial for the correlations in thermal
equilibrium at zero temperature limit but ineffective under the consideration
of the intrinsic decoherence, and these quantities decrease as temperature T
rises on the whole. Besides, J turned out to be constructive, but B be
detrimental in the manipulation and control of various quantities both in
thermal equilibrium and under the intrinsic decoherence which can be avoided by
tuning other system parameters, while D is constructive in thermal equilibrium,
but destructive in the case of intrinsic decoherence in general. In addition,
for the initial state , all
the correlations except the CC, exhibit a damping oscillation to a stable value
larger than zero following the time, while for the initial state , all the correlations monotonously
decrease, but CC still remains maximum. Moreover, there is not a definite
ordering of these quantities in thermal equilibrium, whereas there is a
descending order of the CC, C, GMD and QD under the intrinsic decoherence with
a nonnull B when the initial state is .Comment: 8 pages, 7 figure
Thermal entanglement in the anisotropic Heisenberg model with Dzyaloshinskii-Moriya interaction in an inhomogeneous magnetic field
The thermal entanglement of a two-qubit anisotropic Heisenberg XXZ chain with Dzyaloshinskii-Moriya (DM) interaction in an inhomogeneous magnetic field was studied in detail. The effects of the DM parameter, external magnetic field (B), a parameter b which controls the inhomogeneity of B and the bilinear interaction parameters J(x) = J(y) not equal J(z) (the anisotropic case) on the concurrence (C) was formulated and studied in detail. The behaviors of the concurrences for the cases between (J = J(z) = 1) and (J = -1,J(z) = 1) and, (J = J(z) = -1) and (J = 1,J(z) = -1) at the ground state and at the thermal equilibrium are exactly the same. It was found that for the antiferromagnetic (AFM) case the entanglements persist to higher temperatures in comparison with the ferromagnetic (FM) case. In addition, the AFM case presents a special point at which the nonzero concurrences are all equal at some special temperatures. The further properties will be given in the text