# A Gaussian Theory of Superfluid−Bose-Glass Phase Transition

#### Abstract

We show that gaussian quantum fluctuations, even if infinitesimal, are sufficient to destroy the superfluidity of a disordered boson system in 1D and 2D. The critical disorder is thus finite no matter how small the repulsion is between particles. Within the gaussian approximation, we study the nature of the elementary excitations, including their density of states and mobility edge transition. We give the gaussian exponent η at criticality in 1D and show that its ratio to η of the pure system is universal. PACS numbers: 67.40.Yv, 74.20.Mn, 05.70.Jk, 75.10.Nr Typeset using REVTEX 1 In the presence of disorder, (repulsive) interacting bosons can undergo a transition from the superfluid (SF) phase into an insulating Bose-glass (BG) phase [1] [8]. This transition is intrinsically quantum in nature in that no amount of disorder will destroy the superfluidity without invoking the non-commutativity of density ρ and phase φ. Hence, the usual saddle point or Hartree solution is always long-range ordered, and corresponds to a non-uniform condensate. Given that, it is of interest to investigate what ‘minimal’ quantum effects are necessary to give a transition. In terms of going beyond the saddle point approximation, these effects can be characterized as gaussian, non-linear, topological (as in vortices) etc. In effect, one is asking ‘what drives the transition’, even if the true universality class of the transition may require quantum fluctuations beyond the ‘minimal’ ones. To clarify this perspective, consider the 2D classical XY model as an analogy. There, the true long range order (LRO) is destroyed at any finite temperature by spin waves, even though (bound) vortices do renormalize the exponent η (universality class). That is, spin wave alone can explain why the low temperature phase has algebraically decaying correlations. On the other hand, vortices must be invoked to explain the Kosterlitz-Thouless transition [9]. In this article we show that gaussian fluctuations, even if infinitesimal, are sufficient to destroy superfluidity in 1D and 2D at finite disorder. The model we use is the hard-core boson model with on-site disorder, which is equivalent to the spin-1/2 XY magnet with a transverse random field [1,3,4]. Written in a rotated frame for later convenience, the Hamiltonian is [5]:

### Cite this paper

@inproceedings{Nisamaneephong1993AGT, title={A Gaussian Theory of Superfluid−Bose-Glass Phase Transition}, author={Pornthep Nisamaneephong and Lizeng Zhang and Michael R Ma}, year={1993} }