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The spin-1/2 Ising-Heisenberg tetrahedral chain is exactly solved using itslocal gauge symmetry, which enables one to establish a rigorous mapping withthe corresponding chain of composite Ising spins tractable within thetransfer-matrix approach. Exact results derived for spin-spin correlationfunctions are employed to obtain the frustration temperature, at which aproduct of correlation functions along an elementary triangular plaquettebecomes negative and the relevant spins experience a spin frustration. Inaddition, we have exactly calculated a concurrence quantifying thermalentanglement along with a threshold temperature, above which concurrence as ameasure of thermal entanglement vanishes. It is shown that the frustration andthreshold temperature coincide at sufficiently low temperatures, while theyexhibit a very different behavior in the high-temperature region when tendingtowards completely different asymptotic limits. The threshold temperatureadditionally shows a notable reentrant behavior when it extends over a narrowtemperature region above the classical ground state without any quantumcorrelations. It is demonstrated that the specific heat may display temperaturedependence with or without an anomalous low-temperature peak for a relativelystrong or weak Heisenberg interaction, respectively.

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