Eigenfunction structure and scaling of two interacting particles in the one-dimensional Anderson model
Tóm tắt
The localization properties of eigenfunctions for two interacting particles in the
one-dimensional Anderson model are studied for system sizes up to N = 5000 sites
corresponding to a Hilbert space of dimension ≈107 using the Green function Arnoldi method. The
eigenfunction structure is illustrated in position, momentum and energy representation,
the latter corresponding to an expansion in non-interacting product eigenfunctions.
Different types of localization lengths are computed for parameter ranges in system size,
disorder and interaction strengths inaccessible until now. We confirm that one-parameter
scaling theory can be successfully applied provided that the condition of N being significantly
larger than the one-particle localization length L
1 is verified.
The enhancement effect of the two-particle localization length L
2 behaving as
L
2 ~ L
2
1 is clearly confirmed for a certain quite large interval
of optimal interactions strengths. Further new results for the interaction dependence in a
very large interval, an energy value outside the band center, and different interaction
ranges are obtained.
Tài liệu tham khảo
P.A. Lee, T.V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985)
A. MacKinnon, B. Kramer, Phys. Rev. Lett. 47, 1546 (1981)
A. MacKinnon, B. Kramer, Z. Phys. B 53, 1 (1983)
B. Kramer, A. MacKinnon, Rep. Prog. Phys. 56, 1469 (1993)
K.B. Efetov, Supersymmetry in Disorder and Chaos (Cambridge University Press, 1997)
T. Guhr, A. Müller-Groeling, H.A. Weidenmüller, Phys. Rep. 299, 189 (1998)
C.W.J. Beenakker, Rev. Mod. Phys. 69, 731 (1997)
P.W. Brouwer, K. Frahm, Phys. Rev. B 53, 1490 (1996)
O.N. Dorokhov, Zh. Eksp. Teor. Fiz. 98, 646 (1990) [Sov. Phys. J. Exp. Theor. Phys. 71, 360 (1990)]
D.L. Shepelyansky, Phys. Rev. Lett. 73, 2607 (1994)
M. Screiber, S.S. Hodgman, P. Bordia, H. Lüschen, M.H. Fischer, R. Vosk, E. Altman, U. Schneider, I. Bloch, Science 349, 842 (2015)
Y. Imry, Europhys. Lett. 30, 405 (1995)
D.C. Thouless, Phys. Rev. Lett. 39, 1167 (1977)
K. Frahm, A. Müller-Groeling, J.-L. Pichard, D. Weinmann, Europhys. Lett. 31, 169 (1995)
D. Weinmann, A. Müller-Groeling, J.-L. Pichard, K. Frahm, Phys. Rev. Lett. 75, 1598 (1995)
P. Jacquod, D.L. Shepelyansky, Phys. Rev. Lett. 75, 3501 (1995)
Y.V. Fyodorov, A.D. Mirlin, Phys. Rev. B 52, R11580 (1995)
K. Frahm, A. Müller-Groeling, Europhys. Lett. 32, 385 (1995)
F. Borgonovi, D.L. Shepelyansky, Nonlinearity 8, 877 (1995)
F. Borgonovi, D.L. Shepelyansky, J. Phys. I 6, 287 (1996)
O. Halfpap, A. MacKinnon, B. Kramer, Solid State Commun. 107, 379 (1998)
F. von Oppen, T. Wetting, J. Müller, Phys. Rev. Lett. 76, 491 (1996)
Ph. Jacquod, D.L. Shepelyansky, O.P. Sushkov, Phys. Rev. Lett. 78, 923 (1997)
D.L. Shepelyansky, in Proceedings of les Rencontres de Moriond 1996 on “Correlated Fermions and Transport in Mesoscopic Systems”, edited by T. Martin, G. Montambaux, J. Trân Thanh Vân (Editions Frontières, Gif-sur-Yvette, 1996), p. 201
I.V. Ponomarev, P.G. Silvestrov, Phys. Rev. B 56, 3742 (1997)
R.A. Roemer, M. Schreiber, T. Vojta, Phys. Stat. Sol. B 211, 681 (1999)
K. Frahm, A. Müller–Groeling, J.-L. Pichard, Phys. Rev. Lett. 76, 1509 (1996)
K. Frahm, A. Müller–Groeling, J.-L. Pichard, Z. Phys. B 102, 261 (1997)
J. Richert, H.A. Weidenmüller, J. Phys. A 36, 3281 (2003)
J. Richert, H.A. Weidenmüller, Ann. Phys. 306, 96 (2003)
D. Weinmann, J.-L. Pichard, Phys. Rev. Lett. 77, 1556 (1996)
E. Akkermans, J.-L. Pichard, Eur. Phys. J. B 1, 223 (1998)
X. Waintal, J.-L. Pichard, Eur. Phys. J. B 6, 117 (1998)
X. Waintal, D. Weinmann, J.-L. Pichard, Eur. Phys. J. B 7, 451 (1999)
S. De Toro Arias, X. Waintal, J.-L. Pichard, Eur. Phys. J. B 10, 149 (1999)
R.A. Römer, M. Schreiber, Phys. Rev. Lett. 78, 515 (1997)
R.A. Römer, M. Schreiber, Phys. Rev. Lett. 78, 4890 (1997)
K.M. Frahm, A. Müller-Groeling, J.-L. Pichard, D. Weinmann, Phys. Rev. Lett. 78, 4889 (1997)
P.H. Song, F.V. Oppen, Phys. Rev. B 59, 46 (1999)
P.H. Song, Doochul Kim, Phys. Rev. B 56, 12217 (1997)
M. Leadbeater, R.A. Römer, M. Schreiber, Eur. Phys. J. B 8, 643 (1999)
K.M. Frahm, Eur. Phys. J. B 10, 371 (1999)
D.O. Krimer, R. Khomeriki, S. Flach, J. Exp. Theor. Phys. Lett. 94, 406 (2011)
D.O. Krimer, S. Flach, Phys. Rev. B 91, 100201(R) (2015)
K.M. Frahm, D.L. Shepelyansky, Eur. Phys. J. B 88, 337 (2015)
S. Flach, M. Ivanchenko, R. Khomeriki, Europhys. Lett. 98, 66002 (2012)
G.W. Stewart, Matrix Algorithms Volume II: Eigensystems (SIAM, 2001)
K.M. Frahm, D.L. Shepelyansky, Eur. Phys. J. B 76, 57 (2010)
H.R. Schwartz, Numerische Mathematik (B.G. Teubner, Stuttgart, 1986)
K.M. Frahm, http://www.quantware.ups-tlse.fr/QWLIB/tipdisorder1d, Accessed February (2016)
M. Ortuno, E. Cuevas, Europhys. Lett. 46, 224 (1999)