Interplay between spin frustration and thermal entanglement in the exactly solved Ising-Heisenberg tetrahedral chain

TL;DR

This paper provides an exact analysis of the interplay between spin frustration and thermal entanglement in a solvable Ising-Heisenberg tetrahedral chain, revealing their temperature-dependent behaviors and correlations.

Contribution

It introduces an exact solution method for the Ising-Heisenberg tetrahedral chain and explores the relationship between frustration and thermal entanglement.

Findings

Frustration temperature and threshold temperature coincide at low temperatures.

Threshold temperature exhibits reentrant behavior near the classical ground state.

Specific heat shows different temperature dependencies depending on interaction strength.

Abstract

The spin-1/2 Ising-Heisenberg tetrahedral chain is exactly solved using its local gauge symmetry, which enables one to establish a rigorous mapping with the corresponding chain of composite Ising spins tractable within the transfer-matrix approach. Exact results derived for spin-spin correlation functions are employed to obtain the frustration temperature, at which a product of correlation functions along an elementary triangular plaquette becomes negative and the relevant spins experience a spin frustration. In addition, we have exactly calculated a concurrence quantifying thermal entanglement along with a threshold temperature, above which concurrence as a measure of thermal entanglement vanishes. It is shown that the frustration and threshold temperature coincide at sufficiently low temperatures, while they exhibit a very different behavior in the high-temperature region when tending towards completely different asymptotic limits. The threshold temperature additionally shows a notable reentrant behavior when it extends over a narrow temperature region above the classical ground state without any quantum correlations. It is demonstrated that the specific heat may display temperature dependence with or without an anomalous low-temperature peak for a relatively strong or weak Heisenberg interaction, respectively.