Quantum entanglement at negative temperature

TL;DR

This paper explores quantum entanglement at negative temperatures in spin systems, calculating thermodynamic properties and concurrence, revealing asymmetrical temperature dependence and structure-independent transition points.

Contribution

It provides the first comprehensive calculation of thermodynamic characteristics and entanglement in spin systems across positive and negative temperatures, highlighting structure-independent transition parameters.

Findings

Maximum concurrence occurs at negative temperatures.

Entanglement transition temperatures are structure-independent.

Temperature dependence of concurrence is asymmetrical.

Abstract

An isolated spin system that is in internal thermodynamic equilibrium and that has an upper limit to its allowed energy states can possess a negative temperature. We calculate the thermodynamic characteristics and the concurrence in this system over the entire range of positive and negative temperatures. Our calculation was performed for different real structures, which can be used in experiments. It is found that the temperature dependence of the concurrence is substantially asymmetrical similarly other thermodynamic characteristics. At a negative temperature the maximum concurrence and the absolute temperature of the entanglement appearance are sufficiently larger than those at a positive temperature. The concurrence can be characterized by two dimensionless parameters: by the ratio between the Zeeman and dipolar energies and by the ratio of the thermal and dipolar energies. It was shown that for all considered structures the dimensionless temperatures of the transition between entanglement and separability of the first and second spins are independent of spin structure and number of spins.