Critical Exponents for Three-Dimensional Superfluid--Bose-Glass Phase Transition

TL;DR

This paper investigates the critical exponents of the superfluid--Bose-glass phase transition in three-dimensional disordered lattices using a quantum real-space renormalization-group method, revealing distinct dynamic exponents for different states.

Contribution

It provides the first calculation of the correlation-length and dynamic exponents for this transition in three dimensions, highlighting differences between compressible and incompressible states.

Findings

Dynamic exponent z is 2.5 for compressible states.

Dynamic exponent z is 1.3 for incompressible states.

Correlation-length exponent ν is approximately 1, insensitive to z.

Abstract

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 $\nu$ 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 $\nu$ is shown to be insensitive to z as that in the two-dimensional case, and has value roughly equal to 1.