SU(4) Model of High-Temperature Superconductivity: Manifestation of   Dynamical Symmetry in Cuprates
  The mechanism that leads to high-temperature superconductivity in cuprates remains an open question despite intense study for nearly two decades. Here, we introduce an SU(4) model for cuprate systems having many similarities to dynamical symmetries known to play an important role in nuclear structure physics and in elementary particle physics. Analytical solutions in three dynamical symmetry limits of this model are found: an SO(4) limit associated with antiferromagnetic order; an SU(2) limit that may be interpreted as a d-wave pairing condensate; and an SO(5) limit that may be interpreted as a doorway state between the antiferromagnetic order and the superconducting order. It is demonstrated that with a slightly broken SO(5) but under constraint of the parent SU(4) symmetry, the model is capable of describing the rich physics that is crucial in explaining why cuprate systems that are antiferromagnetic Mott insulators at half filling become superconductors through hole doping. 
Yang Sun, Mike Guidry, Cheng-Li Wu