Finite temperature effects in quantum systems with competing scalar orders

The study of the competition or coexistence of different ground states in many-body systems is an exciting and actual topic of research, both experimentally and theoretically. Quantum fluctuations of a given phase can suppress or enhance another phase depending on the nature of the coupling between the order parameters, their dynamics and the dimensionality of the system. The zero temperature phase diagrams of systems with competing scalar order parameters with quartic and bilinear coupling terms have been previously studied for the cases of a zero temperature bicritical point and of coexisting orders. In this work, we apply theMatsubara summationtechnique from finite temperature quantum field theory to introduce the effects of thermal fluctuations on the effective potential of these systems. This is essential to make contact with experiments. We consider two and three-dimensional materials characterized by a Lorentz invariant quantum critical theory, i.e., with dynamic critical exponentz= 1, such that time and space scale in the same way. We obtain that in both cases, thermal fluctuations lead to weak first-order temperature phase transitions, at which coexisting phases arising from quantum corrections become unstable. We show that above this critical temperature (T_c), the system presents scaling behavior consistent with that approaching a quantum critical point. Below the transition the specific heat has a thermally activated contribution with a gap related to the size of the domains of the ordered phases. We obtain thatT_cdecreases as a function of the distance to the zero temperature classical bicritical point (ZTCBP) in the coexistence region, implying that in our approach, the system attains the highestT_cabove the fine tuned value of this ZTCBP.