Numerical diagonalization analysis of the ground-state superfluid-localization transition in two dimensions

TL;DR

This study uses exact diagonalization to analyze the superfluid-localization transition in a two-dimensional disordered boson system, providing estimates for critical exponents and universal conductivity.

Contribution

It offers the first finite-size scaling analysis of critical exponents and universal conductivity in this system using exact diagonalization methods.

Findings

Correlation-length exponent nu=2.3(0.6)

Dynamical critical exponent z=2

Universal DC conductivity sigma_c(0)=0.135(0.01) ((2e)^2/h)

Abstract

Ground state of the two-dimensional hard-core-boson system in the presence of the quenched random chemical potential is investigated by means of the exact-diagonalization method for the system sizes up to L=5. The criticality and the DC conductivity at the superfluid-localization transition have been controversial so far. We estimate, with the finite-size scaling analysis, the correlation-length and the dynamical critical exponents as nu=2.3(0.6) and z=2, respectively. The AC conductivity is computed with the Gagliano-Balseiro formula, with which the resolvent (dynamical response function) is expressed in terms of the continued-fraction form consisted of Lanczos tri-diagonal elements. Thereby, we estimate the universal DC conductivity as sigma_c(omega=0)=0.135(0.01) ((2e)^2/h).