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 v = 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 consisting of Lanczos tri-diagonal elements. Thereby, we estimate the universal DC conductivity as σc(ω → 0) = 0.135 ± 0.01((2e)2/h).
- 75.10.Jm Quantized spin models
- 75.10.Nr Spin-glass and other random models
- 75.40.Mg Numerical simulation studies
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics