Multifractality of one electron eigenstates in 1D disordered long range models. (English) Zbl 0978.81083
Summary: One investigates the spatial structure of one-electron eigenstates for the one-dimensional Anderson model with long-range off-diagonal disorder \(h_{n,m}=[-1, +1]/n-m^{\delta}\) where \([a,\;b]\) means a uniform random distribution between a and b. Two cases are considered according to the choices for the on-site energy \(\varepsilon_n\), namely, \(\varepsilon_n=0\) and \(\varepsilon_n=[0, 1]\). For \(\delta=1\) all states are critical and the multifractal spectra \(f (\alpha)\) is computed for the states near the center of the band. The level-spacing distribution function is also obtained and its behavior for both small and large separations are studied.
MSC:
| 81V70 | Many-body theory; quantum Hall effect |
| 82B44 | Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics |
References:
| [1] | Anderson, P. W., Phys. Rev., 109, 1492 (1958) |
| [2] | Kramer, B.; MacKinnon, A., Rep. Prog. Phys., 56, 1469 (1993) |
| [3] | Wegner, F., Phys. Rep., 67, 15 (1980) |
| [4] | Wegner, F., Z. Phys. B, 36, 209 (1980) |
| [5] | Hikami, S.; Larkin, A. I.; Nagaoka, Y., Prog. Theor. Phys., 63, 707 (1980) |
| [6] | Abrahams, E.; Anderson, P. W.; Licciardello, D. G.; Ramakrishnan, T. V., Phys. Rev. Lett., 42, 673 (1979) |
| [7] | Mirlin, A. D., Phys. Rev. E, 54, 3221 (1996) |
| [8] | Parshin, D. A.; Schober, H. R., Phys. Rev. B, 57, 10232 (1998) |
| [9] | Cressoni, J. C.; Lyra, M. L., Physica A, 256, 18 (1998) |
| [10] | Schreiber, M.; Grussbach, H., Phys. Rev. Lett., 67, 607 (1991) |
| [11] | Janssen, M., Phys. Rep., 295, 1 (1998) |
| [12] | Kravtsov, V. E.; Muttalib, K. A., Phys. Rev. Lett., 79, 1913 (1997) |
| [13] | Nishigaki, S. M., Phys. Rev. E, 59, 2853 (1999) |
| [14] | Halsey, T. C., Phys. Rev. A, 33, 1141 (1986) |
| [15] | Paladin, G.; Vulpiani, A., Phys. Rep., 156, 147 (1987) |
| [16] | Evangelou, S. N.; Katsanos, D. E., J. Stat. Phys., 85, 5,6 (1996) |
| [17] | Chhabra, A.; Jensen, R. V., Phys. Rev. Lett., 62, 1327 (1989) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
