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

Y. Nishiyama

doi:10.1007/s100510050759

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

Y. Nishiyama

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 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 σ_c(ω → 0) = 0.135 ± 0.01((2e)²/h).

Original language	English
Pages (from-to)	215-223
Number of pages	9
Journal	European Physical Journal B
Volume	9
Issue number	2
DOIs	https://doi.org/10.1007/s100510050759
Publication status	Published - May 2 1999

Keywords

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

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title = "Numerical diagonalization analysis of the ground-state superfluid-localization transition in two dimensions",

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 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).",

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N2 - 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).

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