Strongly disordered superfluids: Quantum fluctuations and critical behavior

Superfluidity may be destroyed by an increasing amount of disorder. The physical systems that may be candidates for this behavior are the superfluid transition of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ in Vycor and the destruction of superconductivity in ‘‘dirty’’ electronic systems. We introduce a model for this phenomenon which may be mapped onto a quantum spin-1/2 model with a random field in the z direction. We study the breakdown of mean-field theory and used a scaling argument to establish the existence of a zero-temperature transition between the superfluid and normal state. We then study the critical behavior of this transition by a mapping onto a (d+1)-dimensional field theory with correlated disorder. The critical behavior of the transition temperature and the superfluid density near the transition point are discussed and scaling relations derived.