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SO(5)-Theory of High-T_{_c} Superconductivity

W. Hanke^{a}, E. Arrigoni^{a}, M. G. Zacher^{a},
and S. C. Zhang^{b}

^{a} Institut fuer theoretische Physik, Universitaet Wuerzburg,
D-97074 Wuerzburg

^{b} Dept. of Physics, Stanford University,
Stanford, CA 94305-4060, USA

hanke@physik.uni-wuerzburg.de
Recent angle-resolved photoemission (ARPES) data, which found evidence for a
d-wave-like modulation of the antiferromagnetic gap, suggest an intimate
interrelation between the antiferromagnetic insulator and the superconductor
with its d-wave gap. This poses a new challenge to microscopic
descriptions, which should account for this correlation between, at first
sight, very different states of matter. Here, we propose a microscopic
mechanism which provides a definite correlation between these two different
gap structures: it is shown that a projected SO(5) theory, which aims at
unifying antiferromagnetism and d-wave superconductivity via a common
symmetry principle while explicitly taking the Mott-Hubbard gap into
account, correctly describes the observed gap characteristics. Specifically,
it accounts for both the dispersion and the order of magnitude difference
between the antiferromagnetic gap modulation and the superconducting gap.
Furthermore, we construct a class of projected SO(5) models, where the
Gutzwiller constraint of no-double-occupancy is implemented exactly. We
introduce the concept of a projected SO(5) symmetry where all static
correlation functions are exactly SO(5) symmetric and discuss the
signature of the projected SO(5) symmetry in dynamical correlation
functions. We show that this class of projected SO(5) models can give a
realistic description of the global phase diagram of the high-T_{c}
superconductors and account for many of their physical properties.