Thermodynamic literature and textbooks consistently treat the unattainability of absolute zero temperature as a fundamental physical principle, as affirmed by the third law of thermodynamics.
We extend the program initiated in [T. Werlang et al., Phys. Rev. Lett. 105, 095702 (2010)] in several directions. Firstly, we investigate how useful quantum correlations, such as entanglement and quantum discord, are in the detection of critical points of quantum phase transitions when the system is at finite temperatures. For that purpose we study several thermalized spin models in the thermodynamic limit, namely, the XXZ model, the XY model, and the Ising model, all of which with an external magnetic field. We compare the ability of quantum discord, entanglement, and some thermodynamic quantities to spotlight the quantum critical points for several different temperatures. Secondly, for some models we go beyond nearest-neighbors and also study the behavior of entanglement and quantum discord for second nearest-neighbors around the critical point at finite temperature. Finally, we furnish a more quantitative description of how good all these quantities are in spotlighting critical points of quantum phase transitions at finite T, bridging the gap between experimental data and those theoretical descriptions solely based on the unattainable absolute zero assumption.
This research aims to introduce a new principle in the flat space-time geometry through the elimination of the classical idea of rest and by including a universal minimum limit of speed in the quantum world. This limit, unattainable by the particles, represents a preferred inertial reference frame associated with a universal background field that breaks Lorentz symmetry. There emerges a new relativistic dynamics where a minimum speed forms an inferior energy barrier. One of the interesting consequences of the existence of such a minimum speed is that it prevents the absolute zero temperature for an ultracold gas according to the third law of thermodynamics. So we will be able to provide a fundamental dynamical explanation for the third law through a connection between such a phenomenological law and the new relativistic dynamics with a minimum speed.
We review the main results and ideas showing that quantum correlations at finite temperatures (T), in particular quantum discord, are useful tools in characterizing quantum phase transitions that only occur, in principle, at the unattainable absolute zero temperature. We first review some interesting results about the behavior of thermal quantum discord for small spin-1/2 chains and show that they already give us important hints of the infinite chain behavior. We then study in detail and in the thermodynamic limit (infinite chains) the thermal quantum correlations for the XXZ and XY models, where one can clearly appreciate that the behavior of thermal quantum discord at finite T is a useful tool to spotlight the critical point of a quantum phase transition.
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