a Study of the Disordered Boson Systems

We investigate disordered boson systems, with emphasis on the effects of disorder on superfluidity. For a system of one dimensional lattice hard-core bosons in a random potential at zero temperature, we demonstrate, exactly, that the superfluid phase is unstable against any amount of disorder. A perturbative study of a weakly interacting disordered boson system is carried out through the Green function method. We obtain the reduction of the speed of sound and the condensate density by (weak) disorder. We also show that randomness can enhance quantum fluctuations and give a finite life time for the Bloch phonons. As the disorder is further increased, a critical point at which a phase transition into a disordered phase will be reached. A disordered lattice hard-core boson model is investigated through a real space renormalization group method to study the critical phenomena of this zero temperature phase transition. Our renormalization group calculation shows the instability of the superfluid phase against any amount of disorder in one dimension, in agreement with the exact result obtained previously. In two and three dimensions, there is a non-trivial fixed point for the renormalization group iteration which separates the superfluid and a disordered phase. The critical exponents upsilon and z are calculated. Our results tend to support the scaling theory prediction of z = d by Fisher et al. We suggest that the finite temperature correction to the singular part of thermodynamic quantities, such as the superfluid density, are exponentially small, based on a finite size scaling analysis for a random T _{rm c} model through a double varepsilon-expansion.