Bose-glass Transition and Spin-Wave Localization for 2D Bosons in a Random Potential

A spin-wave approach of the zero temperature superfluid-insulator transition for two-dimensional hard-core bosons in a random potential mu = +/- W is developed. While at the classical level there is no intervening phase between the Bose-condensed superfluid (SF) and the gapped disordered insulator, the introduction of quantum fluctuations leads to a much richer physics. Upon increasing the disorder strength W, the Bose-condensed fraction disappears first, before the SF. Then a gapless Bose-glass phase emerges over a finite region until the insulator appears. Furthermore, in the strongly disordered SF regime, a mobility edge in the spin-wave excitation spectrum is found at a finite frequency Omega(c) decreasing with W, and presumably vanishing in the Bose-glass phase.