21 research outputs found
Impurity effect on entanglement in an XY two-dimensional spin lattice
AbstractWe consider a finite two dimensional XY spin model. The model consists of a set of seven localized spin-
12 particles in a two dimensional triangular lattice coupled through nearest neighbor exchange interaction in presence of an external magnetic field. We study the effect of a single impurity spin coupled to its nearest neighbor through an exchange interaction J′ on the pairwise entanglement between the different spins in the lattice. We found that when the spin is located at a border site the entanglement between the impurity and its nearest neighbors increases monotonically with J′ reaching a saturation value that depends on the magnetic field strength h. On the other hand the entanglement with the next nearest spins shows a critical behavior where the entanglement increases and then decreases rapidly until it vanishes. The critical coupling value at which the entanglement vanishes increases as h increases. Studying the entanglement between two spins excluding the impurity show that while the entanglement between two spins coupled to the impurity reach a saturation value as J′ increases, it vanishes for spins not coupled to the impurity. Furthermore studying the effect of a central impurity show that the entanglement between nearest neighbor and next nearest neighbor spins reaches an asymptotic value as J′ increases. Interestingly it was demonstrated that the impurity can be used as a switch to control the entanglement between different spins in the lattice turning it on and off
Persistence of entanglement in thermal states of spin systems
We study and compare the persistence of bipartite entanglement (BE) and
multipartite entanglement (ME) in one-dimensional and two-dimensional spin XY
models in an external transverse magnetic field under the effect of thermal
excitations. We compare the threshold temperature at which the entanglement
vanishes in both types of entanglement. We use the entanglement of formation as
a measure of the BE and the geometric measure to evaluate the ME of the system.
We have found that in both dimensions in the anisotropic and partially
anisotropic spin systems at zero temperatures, all types of entanglement decay
as the magnetic field increases but are sustained with very small magnitudes at
high field values. Also we found that for the same systems, the threshold
temperatures of the nearest neighbour (nn) BEs are higher than both of the
next-to-nearest neighbour BEs and MEs and the three of them increase
monotonically with the magnetic field strength. Thus, as the temperature
increases, the ME and the far parts BE of the system become more fragile to
thermal excitations compared to the nn BE. For the isotropic system, all types
of entanglement and threshold temperatures vanish at the same exact small value
of the magnetic field. We emphasise the major role played by both the
properties of the ground state of the system and the energy gap in controlling
the characteristics of the entanglement and threshold temperatures. In
addition, we have shown how an inserted magnetic impurity can be used to
preserve all types of entanglement and enhance their threshold temperatures.
Furthermore, we found that the quantum effects in the spin systems can be
maintained at high temperatures, as the different types of entanglements in the
spin lattices are sustained at high temperatures by applying sufficiently high
magnetic fields.Comment: 20 pages, 17 figure
Entanglement dynamics of one-dimensional driven spin systems in time-varying magnetic fields
We study the dynamics of entanglement for a one-dimensional spin chain with a
nearest neighbor time dependent Heisenberg coupling J(t) between the spins in
presence of a time dependent external magnetic field h(t) at zero and finite
temperatures. We consider different forms of time dependence for the coupling
and magnetic field; exponential, hyperbolic and periodic. We examined the
system size effect on the entanglement asymptotic value. It was found that for
a small system size the entanglement starts to fluctuate within a short period
of time after applying the time dependent coupling. The period of time
increases as the system size increases and disappears completely as the size
goes to infinity. We also found that when J(t) is periodic the entanglement
shows a periodic behavior with the same period, which disappears upon applying
periodic magnetic field with the same frequency. Solving the particular case
where J(t) and h(t) are proportional exactly, we showed that the asymptotic
value of entanglement depends only on the initial conditions regardless of the
form of J(t) and h(t) applied at t > 0.Comment: 22 pages and 8 figure
Entanglement in a Time-Dependent Coupled XY Spin Chain in an External Magnetic Field
We consider an infinite one dimensional anisotropic XY spin chain with a
nearest neighbor time-dependent Heisenberg coupling J(t) between the spins in
presence of a time-dependent magnetic field h(t). We discuss a general solution
for the system and present an exact solution for particular choice of J and h
of practical interest. We investigate the dynamics of entanglement for
different degrees of anisotropy of the system and at both zero and finite
temperatures. We find that the time evolution of entanglement in the system
show non-ergodic and critical behavior at zero and finite temperatures and
different degrees of anisotropy. The asymptotic behavior of entanglement at the
infinite time limit at zero temperature and constant J and h depends only the
parameter lambda=J/h rather than the individual values of J and h for all
degrees of anisotropy but changes for nonzero temperature. Furthermore, the
asymptotic behavior is very sensitive to the initial values of J and h and for
particular choices we may create finite asymptotic entanglement regardless of
the final values of J and h. The persistence of quantum effects in the system
as it evolves and as the temperature is raised is studied by monitoring the
entanglement. We find that the quantum effects dominates within certain regions
of the kT-lambda space that vary significantly depending on the degree of the
anisotropy of the system. Particularly, the quantum effects in the Ising model
case persists in the vicinity of both its critical phase transition point and
zero temperature as it evolves in time. Moreover, the interplay between the
different system parameters to tune and control the entanglement evolution is
explored.Comment: 33 pages, 17 figures; v3: Grammar errors and typos corrected, Figure
17(b) update
Nuclear-induced time evolution of entanglement of two-electron spins in anisotropically coupled quantum dot
We study the time evolution of entanglement of two spins in anisotropically
coupled quantum dot interacting with the unpolarized nuclear spins environment.
We assume that the exchange coupling strength in the z-direction is
different from the lateral one . We observe that the entanglement decays
as a result of the coupling to the nuclear environment and reaches a saturation
value, which depends on the value of the exchange interaction difference between the two spins and the strength of the applied external
magnetic field. We find that the entanglement exhibits a critical behavior
controlled by the competition between the exchange interaction and the
external magnetic field. The entanglement shows a quasi-symmetric behavior
above and below a critical value of the exchange interaction. It becomes more
symmetric as the external magnetic field increases. The entanglement reaches a
large saturation value, close to unity, when the exchange interaction is far
above or below its critical value and a small one as it closely approaches the
critical value. Furthermore, we find that the decay rate profile of
entanglement is linear when the exchange interaction is much higher or lower
than the critical value but converts to a power law and finally to a Gaussian
as the critical value is approached from both directions. The dynamics of
entanglement is found to be independent of the exchange interaction for
isotropically coupled quantum dot.Comment: 24 pages and 7 figures. v3: major change
Tuning entanglement and ergodicity in two-dimensional spin systems using impurities and anisotropy
We consider the entanglement in a two-dimensional XY model in an external magnetic field h. The model consists of a set of seven localized spin-1/2 particles in a two-dimensional triangular lattice coupled through nearest-neighbor exchange interaction J. We examine the effect of single and double impurities in the system as well as the degree of anisotropy on the nearest-neighbor entanglement and ergodicity of the system. We have found that the entanglement of the system at the different degrees of anisotropy mimics that of the one-dimensional spin systems at the extremely small and large values of the parameter lambda = h/J. The entanglement of the Ising and partially anisotropic systems shows phase transition in the vicinity of lambda = 2, whereas, the entanglement of the isotropic system suddenly vanishes there. Also, we investigate the dynamic response of the system containing single and double impurities to an external exponential magnetic field at different degrees of anisotropy. We have demonstrated that the ergodicity of the system can be controlled by varying the strength and location of the impurities as well as the degree of anisotropy of the coupling