SO(5) theory

Superconductivity in the cuprates is characterized by its proximity to the antiferromagnetic phase.(See Fig.1.) This obviously tells us that in these materials, the tendency towards superconductivity (SC) is in competition with that towards antiferromagnetism (AF). An attractive way of viewing high temperature superconductivity (HTSC) which emphasizes this aspect was put forth by Stanford physicist S. C. Zhang in 1997. In his SO(5) theory, the 3 components of the antiferromagnetic order parameter (OP) and the 2 for the superconducting OP are grouped into a 5-component "superspin" which represents a unified OP for SC and AF; its direction specifies the state which is realized (Fig.2). The framework predicts a mode which oscillates between the SC and AF sectors, which very well may correspond to a feature observed in neutron scattering experiments.

Fig.1: schematic picture of the phase diagram of high-Tc superconductor

Fig2: picture of 5-component superspin

Fig.3

Fig.4

Extending our previous methods and experience to simulate the 2-component order parameter of the superconductor (i.e. the XY model) to the 5-component superspin, we have conducted extensive numerical studies of a lattice version of the SO(5) theory. We believe our results are noteworthy; phase diagrams for part of our work are displayed. Our results should also be relevant to the phase diagrams of organic superconductors where similar behavior has been observed.

Recent work has focused on the bicritical phenomenna between the AF and SC phases, a hallmark of the SO(5) theory(Fig.3).Besides successfully computing the critical exponent upon the approach to the bicritical point (which will let experiments decide whether they are indeed observing the trace of the "number 5" of the theory), we have demonstrated that the bicritical point is stable with respect to repusive AF-SC fluctuations, contrary to the epsilon-expansion results.

Figure 4 depicts the phase diagram for the case with an applied magnetic field. We find a tricitical point on the Neel transition line ( N(normal) to AF ) at which the transition switches from first to second order. The effect of superconducting fluctuations is responsible for the change to the first order transition, an important implication of the SO(5) theory.