Critical exponents for the three-dimensional superfluid-Bose-glass phase transition.

The critical phenomenon of the zero temperature superfluid−Bose-glass phase transition for hard-core bosons on a three-dimensional disordered lattice is studied using a quantum real-space renormalization-group method. The correlation-length exponent ν and the dynamic exponent z are computed. The critical exponent z is found to be 2.5 for compressible states and 1.3 for incompressible states. The exponent ν is shown to be insensitive to z as that in the two-dimensional case, and has value roughly equal to 1.