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Resonating-valence-bond structure of Gutzwiller-projected superconducting wave functions
Gutzwiller-projected (GP) wave functions have been widely used for describing
spin-liquid physics in frustrated magnets and in high-temperature
superconductors. Such wave functions are known to represent states of the
resonating-valence-bond (RVB) type. In the present work I discuss the RVB
structure of a GP singlet superconducting state with nodes in the spectrum. The
resulting state for the undoped spin system may be described in terms of the
"path integral" over loop coverings of the lattice, thus extending the known
construction for RVB states. The problem of the topological order in GP states
may be reformulated in terms of the statistical behavior of loops. The simple
example of the projected d-wave state on the square lattice demonstrates that
the statistical behavior of loops is renormalized in a nontrivial manner by the
projection.Comment: 6 pages, 4 figures, some numerical data adde
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