| e study the nature of various quantum phase transitions corresponding to the onset of superfluidity, at zero temperature, of bosons in a quenched medium. Particle-hole symmetry plays an essential role in determining the universality class of the transitions. We may include disorder in the local chemical potentials or site energies, and also the hopping strengths. We then distinguish three cases: (i) exact particle-hole symmetry, in which the site energies all vanish, (ii) statistical particle-hole symmetry in which the site energy distribution is symmetric about zero and hence vanishes on average, and (iii) complete absence of particle-hole symmetry in which the distribution is generic. We explore in each case the nature of the excitations in the nonsuperfluid Bose glass phase. We then focus on the critical point and discuss the validity of various scaling arguments. We argue that statistical particle-hole symmetry is restored on large scales close to the critical point, and case (ii) therefore describes the dirty boson fixed point. Particle-hole asymmetry of type (iii) is irrelevant. Using various duality transformations we verify these ideas in one dimension. To study higher dimensions we attempt to generalize the Dorogovtsev-Cardy-Boyonovsky double epsilon expansion technique to this problem. We find that when the dimension of time... |
