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An SU(4) model of high-temperature superconductivity and antiferromagnetismhas recently been proposed. The SO(5) group employed by Zhang is embedded inthis SU(4) as a subgroup, suggesting a connection between our SU(4) model andthe Zhang SO(5) model. In order to understand the relationship between the thetwo models, we have used generalized coherent states to analyze the nature ofthe SO(5) subgroup. By constructing coherent-state energy surfaces, wedemonstrate explicitly that the SU(4) supset SO(5) symmetry can be interpretedas a critical dynamical symmetry interpolating between superconducting andantiferromagnetic phases, and that this critical dynamical symmetry has manysimilarities to critical dynamical symmetries identified previously in otherfields of physics. More generally, we demonstrate with this example that themathematical techniques associated with generalized coherent states may havepowerful applications in condensed matter physics because they provide a clearconnection between microscopic many-body theories and their broken-symmetryapproximate solutions. In addition, these methods may be interpreted asdefining the most general Bogoliubov transformation subject to a Lie groupsymmetry constraint, thus providing a mathematical connection between algebraicformulations and the language of quasiparticle theory. Finally, we suggest thatthe identification of the SO(5) symmetry as a critical dynamical symmetryimplies deep algebraic connections between high-temperature superconductors andseemingly unrelated phenomena in other field of physics.Comment: 12 pages, 2 figures, final version accepted by Phys. Rev.

SO(5) as a critical dynamical symmetry in the SU(4) model of high-temperature superconductivity