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

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.