Static and dynamical quantum correlations in phases of an alternating field XY model

TL;DR

This paper explores static and dynamic quantum entanglement in an alternating field XY model, revealing phase detection via entanglement derivatives, a factorization line, temperature effects, and ergodic behavior of entanglement.

Contribution

It introduces analysis of a three-phase XY model with an alternating field, identifying a factorization line and examining entanglement dynamics and ergodicity in this system.

Findings

First derivative of bipartite entanglement detects all three phases.

Identifies a factorization line where the state is separable.

Entanglement exhibits non-monotonic temperature dependence in certain phases.

Abstract

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 non-monotonic behavior of entanglement with respect to temperature in the anti-ferromagnetic 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 non-ergodic, depending on the system parameters.