Abstract.
In this paper we study the localization transition induced by the disorder in random antiferromagnetic spin-\(\frac{1}{2}\) chains. The results of numerical large scale computations are presented for the XX model using its free fermions representation. The scaling behavior of the spin stiffness is investigated for various disorder strengths. The disorder dependence of the localization length is studied and a comparison between numerical results and bosonization arguments is presented. A non trivial connection between localization effects and the crossover from the pure XX fixed point to the infinite randomness fixed point is pointed out.
Similar content being viewed by others
References
H. Bethe, Z. Physik 71, 205 (1931)
N.D. Mermin, H. Wagner, Phys. Rev. Lett. 17, 1133(1966)
C.J. Hamer, G.R.W. Quispel, M.T. Batchelor, J. Phys. A 20, 5677 (1987); F. Woynarovich, H.-P. Eckle, J. Phys. A 20, L97 (1987); F.C. Alcaraz, M.N. Barber, M.T. Batchelor, Ann. Phys. 182, 280 (1988)
N. Byers, C.N. Yang, Phys. Rev. Lett. 7, 46 (1961)
B.S. Shastry, B. Sutherland, Phys. Rev. Lett. 65, 243 (1990); B. Sutherland, B.S. Shastry, Phys. Rev. Lett. 65, 1833 (1990)
T.M.R. Byrnes, R.J. Bursill, H.-P. Eckle, C.J. Hamer, A.W. Sandvik, Phys. Rev. B 66, 195313 (2002)
S. Eggert, I. Affleck, Phys. Rev. B 46, 10866 (1992); S. Eggert, I. Affleck, Phys. Rev. Lett. 75, 934 (1995)
C.L. Kane, M.P.A. Fisher, Phys. Rev. Lett. 68, 1220 (1992); C.L. Kane, M.P.A. Fisher, Phys. Rev. Lett. 46, 15233 (1992)
C.A. Doty, D.S. Fisher, Phys. Rev. B 45, 2164 (1992)
E. Abrahams, P.W. Anderson, D.C. Licciardello, T.V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979)
T. Giamarchi, H.J. Schulz, Phys. Rev. B 37, 325 (1988)
N. Laflorencie, H. Rieger, Phys. Rev. Lett. 91, 229701 (2003)
N. Laflorencie, H. Rieger, A.W. Sandvik, P. Henelius, preprint cond-mat/0312572
K. Hamacher, J. Stolze, W. Wenzel, Phys. Rev. Lett. 89, 127202 (2002)
O. Montrunich, K. Damle, D. Huse, Phys. Rev. B 63, 134424 (2001)
G. Bouzerar, D. Poilblanc, G. Montambaux, Phys. Rev. B 49, 8258 (1994)
K.J. Runge, G.T. Zimanyi, Phys. Rev. B 49, 15212 (1994)
T. Giamarchi, B.S. Shastry, Phys. Rev. B 51, 10915 (1995)
P. Schmitteckert et al. , Phys. Rev. Lett. 80, 560 (1998)
L. Urba, A. Rosengren, Phys. Rev. B 67, 104406 (2003)
F. Schütz, M. Kollar, P. Kopietz, Phys. Rev. Lett. 91, 017205 (2003)
I. Affleck, P. Simon, Phys. Rev. Lett. 86, 2854 (2001); P. Simon, I. Affleck, Phys. Rev. Lett. 89, 206602 (2002)
W.G. van der Wiel et al. , Science 289, 2105 (2000); J. Nygard, D.H. Cobden, P.E. Lindelof, Nature (London) 408, 342 (2000)
A.P. Young, H. Rieger, Phys. Rev. B 53, 8486 (1996)
E. Lieb, T. Schulz, D. Mattis, Ann. Phys. (NY) 16, 407 (1961)
N. Laflorencie, S. Capponi, E.S. Sorensen, Eur. Phys. J. B 24, 77 (2001)
The linear algebra package LAPACK has been used here
P. Henelius, S.M. Girvin, Phys. Rev. B 57, 11457 (1998)
F. Igloi, R. Juhász, H. Rieger, Phys. Rev. B 61, 11552 (2000)
D.S. Fisher, Phys. Rev. B 50, 3799 (1994)
M. Wallin, E.S. Sørensen, S.M. Girvin, A.P. Young, Phys. Rev. B 49, 12115 (1994)
Strictly speaking there is a logaritmic correction but it is subdominant
Author information
Authors and Affiliations
Corresponding author
Additional information
Received: 6 February 2004, Published online: 12 August 2004
PACS:
75.10.Jm Quantized spin models - 75.40.Mg Numerical simulation studies - 05.70.Jk Critical point phenomena - 75.50.Lk Spin glasses and other random magnets
Rights and permissions
About this article
Cite this article
Laflorencie, N., Rieger, H. Scaling of the spin stiffness in random spin- \(\frac{\mathsf 1}{\mathsf 2}\) chains. Eur. Phys. J. B 40, 201–207 (2004). https://doi.org/10.1140/epjb/e2004-00258-x
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2004-00258-x