Thermal entanglement of one-dimensional Heisenberg quantum spin chains in magnetic fields

TL;DR

This paper investigates the thermal entanglement in one-dimensional Heisenberg spin chains under magnetic fields, revealing temperature thresholds for entanglement disappearance and contrasting behaviors in different interaction types.

Contribution

It provides exact and numerical analyses of thermal entanglement in Heisenberg chains, introducing a thermal witness and exploring field effects on entanglement.

Findings

Thermal entanglement vanishes at a temperature ~0.4843J, independent of magnetic field.

Distinct behaviors of entanglement in antiferromagnetic and ferromagnetic interactions.

Field-dependent changes in the vanishing temperature of entanglement for F interactions.

Abstract

The thermal pairwise entanglement (TE) of the S=1/2 XY chain in a transverse magnetic field is exactly resolved by means of the Jordan-Wigner transformation. It is found that the TE vanishes at a common temperature Tc~0.4843J, which is irrelevant to the field. A thermal quantity is proposed to witness the entangled state. Furthermore, the TE of the S=1/2 antiferromagnetic-ferromagnetic (AF-F) Heisenberg chain is studied by the transfer-matrix renormalization group method.The TEs of the spins coupled by AF and F interactions are found to behave distinctively. The vanishing temperature of the field-induced TE of the spins coupled by F interactions is observed to change with the magnetic field. The results are further confirmed and analyzed by the mean-field theory.