Strongly disordered superfluids: Quantum fluctuations and critical behavior

Abstract

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.