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

Relativistic corrections to the nuclear Schiff moment

Parity and time invariance violating ($P,T$-odd) atomic electric dipole moments (EDM) are induced by interaction between atomic electrons and nuclear $P,T$-odd moments which are produced by $P,T$-odd nuclear forces. The nuclear EDM is screened by atomic electrons. The EDM of a non-relativistic atom with closed electron subshells is induced by the nuclear Schiff moment. For heavy relativistic atoms EDM is induced by the nuclear local dipole moments which differ by 10-50% from the Schiff moments calculated previously. We calculate the local dipole moments for ${^{199}{\rm Hg}}$ and ${^{205}{\rm Tl}}$ where the most accurate atomic and molecular EDM measurements have been performed.Comment: 3 pages, no figures, brief repor