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.

• Received 11 July 2016

DOI:https://doi.org/10.1103/PhysRevA.94.042310