Phase diagrams in the SO(5) quantum rotor theory of high-Tcsuperconductivity

Using the spherical approach for the three-dimensional quantum rotor we have studied the thermodynamic properties of Zhang’s SO(5) quantum rotor theory. We have performed a non-mean-field treatment of the lattice version of the nonlinear quantum $\sigma$ model and discussed possible scenarios for temperature-doping phase diagrams. The model considered can contain large SO(5) anisotropy parameters (like spin, charge, and so-called $“\pi ”$ susceptibilities which regulate the strength of the quantum fluctuations). It is found that the topology of the temperature-chemical-potential $(T-\mu )$ phase diagrams assumes different forms depending on the strength of the quantum fluctuations. In the SO(5)-symmetric kinetic energy model we established the condition for the existence of the quantum critical point separating anitiferromagnetic and superconducting states at zero temperature. In the intermediate quantum fluctuation regime there is a first-order transition between the antiferromagnetic and superconducting phases. For the class of models with an asymmetric kinetic energy parts we found no evidence for the existence of the intermediate mixed so-called “spin bag” phase in the $T-\mu$ phase diagram.