Correlations in doped antiferromagnets

A comprehensive Study of doped resonating valence bond states is performed. It reveals a fundamental connection between superconductivity and quantum spin fluctuations in underdoped cuprates: Cooper pair hopping strongly redu ces the local magnetization m(0). This effect pertains to recent muon spin rotation measurements in which m(0) varies weakly with hole doping in the p oorly conducting regime, but drops precipitously above the onset of superco nductivity. The Gutzwiller mean field approximation (GA) is found to agree with numerical Monte Carlo calculations. The GA shows, for example, that fo r a bond amplitude u(r) =e(-r/xi), spin-spin correlations decay exponential ly with a correlation length proportional to e(3 pi xi 2/2). The expectatio n value of the Heisenberg model is found to be correlated with the average loop density.