We investigate the dynamics of entanglement, quantum correlation and classical correlation for the one-dimensional XY model in a transverse magnetic field. With the initial state polarized along the z axis, we find that the first maximum of the classical correlation between the nearest neighbor sites peaks around the critical point for large anisotropy parameter. It may indicate the quantum phase transition. For all kinds of correlation, we find that their behaviors between the nearest neighbor sites are significantly different from those of the next-nearest neighbor sites.
We study the dynamics of entanglement for the XY-model, one-dimensional spin systems coupled through the nearest neighbor exchange interaction and subject to an external time-dependent magnetic field. Using the two-site density matrix, we calculate the time-dependent entanglement of formation between nearest neighbor qubits. We investigate the effect of varying the temperature, the anisotropy parameter and the external time-dependent magnetic field on the entanglement. We have found that the entanglement can be localized between nearest neighbor qubits for certain values of the external time-dependent magnetic field. Moreover, as known for the magnetization of this model, the entanglement shows nonergodic behavior, it does not approach its equilibrium value at the infinite time limit.
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.
Abstract In this study, a spin-1/2 extended anisotropic XY chain has been introduced in which both time reversal and SU(2) symmetries are broken but Z 2 symmetry is preserved. Magnetic and topological phase diagrams in the parameter space have been drawn in the presence of transverse magnetic field. Entanglement measures like mutual information and quantum discord are also evaluated and it indicates that these transitions are second order in nature. Quantum phase transition is noted at zero magnetic field, as well as magnetic long range order is found to withstand magnetic field of any strength. Exact analytic results for spin-spin correlation functions have been obtained in terms of Jordan-Wigner fermionization. Existence of long range magnetic order has been investigated numerically by finding correlation functions as well as the Binder cumulant in the ground state. Dispersion relation, ground state energy, and energy gap are obtained analytically. In order to find the topologically nontrivial phase, sign of Pfaffian invariant and value of winding number have been evaluated. Both magnetic and topological phases are robust against the magnetic field and found to move coercively in the parameter space with the variation of its strength. Long range orders along two orthogonal directions and two different topological phases are found and their one-to-one correspondence has been found. Finally casting the spinless fermions onto Majorana fermions, properties of zero energy edge states are studied. Three different kinds of Majorana pairings are noted. In the trivial phase, next-nearest-neighbor Majorana pairing is found, whereas two different types of nearest-neighbor Majorana pairings are identified in the topological superconducting phase.
We investigate the static and dynamical patterns of entanglement in an anisotropic
XY model with an alternating transverse magnetic field, which is equivalent to a two-component one-dimensional Fermi gas on a lattice, a system realizable with current technology. Apart from the antiferromagnetic and paramagnetic phases, the model possesses a dimer phase which is not present in the transverse
XY model. At zero temperature, we find that the first derivative of bipartite entanglement can detect all the three phases. We analytically show that the model has a ``factorization line'' on the plane of system parameters, in which the zero-temperature state is separable. Along with investigating the effect of temperature on entanglement in a phase plane, we also report a nonmonotonic behavior of entanglement with respect to temperature in the antiferromagnetic and paramagnetic phases, which is surprisingly absent in the dimer phase. Since the time dynamics of entanglement in a realizable physical system plays an important role in quantum information processing tasks, the evolutions of entanglement at small as well as large time are examined. Consideration of large-time behavior of entanglement helps us to prove that in this model, entanglement is always ergodic. We observe that other quantum correlation measures can qualitatively show similar features in zero and finite temperatures. However, unlike nearest-neighbor entanglement, the nearest-neighbor information-theoretic measures can be both ergodic as well as nonergodic, depending on the system parameters.
We study the evolution of nearest-neighbor entanglement in the one-dimensional Ising model with an external transverse field. The system is initialized as the so-called thermal ground state of the pure Ising model. We analyze properties of the generation of entanglement for different regions of external transverse fields. We find that the derivative of the time at which the entanglement reaches its first maximum with respect to the reciprocal transverse field has a minimum at the critical point. This is an indicator of quantum phase transition.