Real-space renormalization-group study of hard-core dirty bosons

We investigate the critical phenomena of hard-core bosons in a disordered medium. Such a system is mapped onto a quantum spin-1/2 XY model with transverse random field. The system then is studied through a quantum real-space renormalization-group method. We find that randomness is always relevant in a one-dimensional (1D) system, in agreement with exact results. In two and three dimensions, there is a critical amount of disorder, below which the superfluid phase is stable. In 2D, the dynamic exponent z=1.7 for compressible states, and is close to the value of z=d as predicted by Fisher et al. $z— is smaller for incompressible states. The correlation length exponent ν is insensitive to z, and roughly equals 1.4. Unlike the superfluid–Mott-insulator transition without disorder, which has two distinct universality classes, we find there is only one universality class for the superfluid–Bose-glass transition.