We study the dynamics evolution of a two-quhit Heisenherg XXX spin chain under a time-dependent rotating magnetic field. Based on the algebraic structure of the non-autonomous system, the exact solution of the Schrödinger equation is obtained by using the method of algebraic dynamics. Based on the time-dependent analytical solution, we further study the entanglement evolution between the two coupled spins for different initial states, and find that the entanglement is determined by the coefficients of the initial state and the coupling constant J of the system.
The Heisenberg spin cluster with two particles controlled by a time-dependent magnetic field is investigated. Since the system possesses an SU（2） algebraic structure, the exact analytical solution to time evolution operator can be obtained by using algebraic dynamical method. Based on the analytical solution, the time evolution of wave function of the two-particle system can be obtained, then the entanglement can be calculated easily. The time evolution of the entanglement for different initial states is studied, and the effect of external field on the entanglement is discussed as well.
We study the dynamics of a two-qubit system coupled through time dependent anisotropic
XYZ Heisenberg interaction in presence of a time varying non-uniform external magnetic field. Exact results are presented for the time evolution of the system under certain integrability conditions. Furthermore, the corresponding entanglement of the system is studied for different values of the involved parameters. We found that the time evolution and different properties of entanglement such as amplitude, frequency and profile can be finely tuned by the interplay of the characteristics of the time-dependent magnetic field and exchange coupling. Also we show how the discrete symmetries of the system Hamiltonian, which splits its Hilbert space into two distinct subspaces, can be utilized to deduce the dynamics in one of its two distinct subspaces from the other one. Moreover, approximate results for the time evolution are provided utilizing the rotating wave as well as the perturbation approximations for the special case of either static magnetic field or exchange coupling. We compare the range of validity of the two approximation methods and their effectiveness in treating the considered system and determine their critical parameters.
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 shows nonergodic 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 $\ensuremath{\lambda}=J/h$ 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 dominate within certain regions of the
kT-$\ensuremath{\lambda}$ space that vary significantly depending on the degree of the anisotropy of the system. Particularly, the quantum effects in the Ising model case persist 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.
We propose a new approach called Ket-Bra Entangled State (KBES) Method for converting master equation into Schrödinger-like equation. With this method, we investigate decoherence process and entanglement dynamics induced by a
2-qubit spin chain that each qubit coupled with reservoir. The spin chain is an anisotropy
XYZ Heisenberg model in the external magnetic field
B, the corresponding master equation is solved concisely by KBES method; Furthermore, the effects of anisotropy, temperature, external field and initial state on concurrence dynamics is analyzed in detail for the case that initial state is Extended Wenger-Like(EWL) state. Finally we research the coherence and concurrence of the final state (namely the density operator for time tend to infinite)
We study the dynamics of nearest-neighbor entanglement for a one-dimensional spin chain with a nearest-neighbor time-dependent Heisenberg coupling
J(t) between the spins in the 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. Solving the system numerically, 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. Testing the effect of the transition constant for an exponential or hyperbolic coupling showed a direct impact on the asymptotic value of the entanglement; the larger the constant is, the lower the asymptotic value and the more rapid decay of entanglement are, which confirms the nonergodic character of the system. 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 case $J(t)=\ensuremath{\lambda}h(t)$, for constant $\ensuremath{\lambda}$, exactly, we showed that the time evolution and asymptotic value of entanglement are dictated solely by the parameter $\ensuremath{\lambda}=J/h$ rather than the individual values of
J and
h, not only when they are time independent and at zero temperature, but also when they are time dependent but proportional at zero and finite temperatures for all degrees of anisotropy.