  In [Phys. Rev. A 107, 052420 (2023)] we showed that the quantum teleportation
protocol can be used to detect quantum critical points (QCPs) associated with a
couple of different classes of quantum phase transitions, even when the system
is away from the absolute zero temperature (T=0). Here, working in the
thermodynamic limit (infinite chains), we extend the previous analysis for
several other spin-1/2 models. We investigate the usefulness of the quantum
teleportation protocol to detect the QCPs of those models when the temperature
is either zero or greater than zero. The spin chains we investigate here are
described by the XXZ model, the XY model, and the Ising model, all of them
subjected to an external magnetic field. Specifically, we use a pair of nearest
neighbor qubits from an infinite spin chain at thermal equilibrium with a
reservoir at temperature T as the resource to execute the quantum teleportation
protocol. We show that the ability of this pair of qubits to faithfully
teleport an external qubit from the chain is dramatically affected as we cross
the QCPs related to the aforementioned models. The results here presented
together with the ones of [Phys. Rev. A 107, 052420 (2023)] suggest that the
quantum teleportation protocol is a robust and quite universal tool to detect
QCPs even when the system of interest is far from the absolute zero
temperature.
