RT Journal Article
T1 Anderson transition in low-dimensional disordered systems driven by long-range nonrandom hopping
A1 Rodriguez, A.
A1 Malyshev, Andrey
A1 Sierra, G.
A1 Martin-Delgado Alcántara, Miguel Ángel
A1 Rodriguez-Laguna, J.
A1 Domínguez-Adame Acosta, Francisco
AB The single-parameter scaling hypothesis predicts the absence of delocalized states for noninteracting quasiparticles in low-dimensional disordered systems. We show analytically, using a supersymmetric method combined with a renormalization group analysis, as well as numerically that extended states may occur in the one- and two-dimensional Anderson model with a nonrandom hopping falling off as some power of the distance between sites. The different size scaling of the bare level spacing and the renormalized magnitude of the disorder seen by the quasiparticles finally results in the delocalization of states at one of the band edges of the quasiparticle energy spectrum.
PB American Physical Society
SN 0031-9007
YR 2003
FD 2003-01-17
LK https://hdl.handle.net/20.500.14352/51262
UL https://hdl.handle.net/20.500.14352/51262
LA eng
NO [1] P.W. Anderson, Phys. Rev. 109, 1492 (1958).[2] E. Abrahams, P.W. Anderson, D. C. Licciardello, and V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).[3] P. A. Lee and T.V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985).[4] B. Kramer and A. MacKinnon, Rep. Prog. Phys. 56, 1469 (1993).[5] D. E. Logan and P. G. Wolynes, Phys. Rev. B 29, 6560 (1984); 31, 2437 (1985); 36, 4135 (1987); J. Chem. Phys. 87, 7199 (1987).[6] L. S. Levitov, Europhys. Lett. 9, 83 (1989); Ann. Phys. (Leipzig) 8, 697 (1999).[7] A. D. Mirlin, Y.V. Fyodorov, F.-M. Dittes, J. Quezada, and T. H. Seligman, Phys. Rev. E 54, 3221 (1996).[8] D. A. Parshin and H. R. Schober, Phys. Rev. B 57, 10 232 (1998).[9] L. I. Deych, A. A. Lisyansky, and B. L. Altshuler, Phys. Rev. Lett. 84, 2678 (2000); Phys. Rev. B 64, 224202 (2001).[10] A. Nabetani, A. Tamioka, H. Tamaru, and K.. Miyano, J. Chem. Phys. 102, 5109 (1995).[11] R. Kopelman, M. Shortreed, Z.-Y. Shi, W. Tan, Z. Xu, J. Moore, A. Bar-Haim, and J. Klafter, Phys. Rev. Lett. 78, 1239 (1997).[12] M. A. Martín-Delgado, J. Rodríguez-Laguna, and G. Sierra, Phys. Rev. B 65, 155116 (2002); cond-mat/0012382.[13] A. Rodríguez, V. A. Malyshev, and F. DomínguezAdame, J. Phys. A 33, L161 (2000).[14] K. B. Efetov, Adv. Phys. 32, 53 (1983).[15] S. Guruswamy, A. LeClair, and A.W.W. Ludwig, Nucl. Phys. B583, 475 (2000).[16] R. Shankar, Rev. Mod. Phys. 66, 129 (1994).[17] A.W.W. Ludwig, M. P. A. Fisher, R. Shankar, and G. Grinstein, Phys. Rev. B 50, 7526 (1994).[18] G. H. Golub and C. F. Van Loan, Matrix Computations (The Johns Hopkins University Press, Maryland, 1996).[19] M. A. Martín-Delgado, G. Sierra, and R. M. Noack, J. Phys. A 32, 6079 (1999)
NO © 2003 The American Physical Society. V. A. M. acknowledges support from MECyD (Project No. SAB2000-0103). A. R. and F. D-A. were supported by DGI-MCyT (Project No. MAT2000-0734) and CAM (Project No. 07N/0075/2001). G. S. and M. A. M-D. acknowledge support from PGC (Project No. BFM2000-1320-C02-01).
NO MECyD
NO DGI-MCyT
NO CAM
NO PGC
DS Docta Complutense
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