Persistence of entanglement in thermal states of spin systems

TL;DR

This study investigates how bipartite and multipartite entanglement in spin XY models persists under thermal effects, revealing the influence of magnetic fields, system anisotropy, and impurities on entanglement robustness at finite temperatures.

Contribution

It provides a comparative analysis of entanglement persistence in 1D and 2D spin systems, highlighting the effects of magnetic fields, anisotropy, and impurities on entanglement thresholds and robustness.

Findings

Nearest neighbor entanglement has higher threshold temperatures than longer-range entanglements.

Entanglement persists at high temperatures with strong magnetic fields.

Impurities can enhance and preserve entanglement at finite temperatures.

Abstract

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.