Abstract
We consider isotropic spin-1/2 two-leg ladders with dominant spatially-modulated rung exchanges. We study the effect of a uniform magnetic field on the ground state phase diagram of the model using perturbation theory and the numerical Lanczos method. The ground state phase diagram consists of two gapless Luttinger liquid (LL) and three gapped phases. Numerically, we calculate the concurrence between two spins and the entanglement entropy between legs. Numerical experiment shows that the gapless LL phases are fundamentally different. In the first LL phase, only spins on rungs are entangled, but in the second LL phase the spins on legs are long-distance entangled. Therefore, the concurrence between spins on legs can be considered as a function to distinguish the LL phases.
Similar content being viewed by others
References
For a review see E. Dagotto, Rep. Prog. Phys. 62, 1525 (1999)
E. Dagotto, T.M. Rice, Science 271, 618 (1996)
R. Chitra, T. Giamarchi, Phys. Rev. B 55, 5816 (1997)
D.C. Cabra, A. Honecker, P. Pujol, Phys. Rev. Lett. 79, 5126 (1997)
D.C. Cabra, A. Honecker, P. Pujol, Phys. Rev. B 58, 6241 (1998)
F. Mila, Eur. Phys. J. B 6, 201 (1998)
K. Totsuka, Phys. Rev. B 57, 3454 (1998)
M. Usami, S.I. Suga, Phys. Rev. B 58, 14401 (1998)
T. Giamarchi, A.M. Tsvelik, Phys. Rev. B 59, 11398 (1999)
M. Hagiwara, H.A. Katori, U. Schollwöck, H.-J. Mikeska, Phys. Rev. B 62, 1051 (2000)
X. Wang, l. Yu, Phys. Rev. Lett. 84, 5399 (2000)
T. Hikihara, A. Furusaki, Phys. Rev. B 63, 134438 (2001)
S. Wessel, M. Olshanii, S. Hass, Phys. Rev. Lett. 87, 206407 (2001)
Y.-J. Wang, F.H.L. Essler, M. Fabrizio, A.A. Nersesyan, Phys. Rev. B 66, 024412 (2002)
Y.-J. Wang, Phys. Rev. B 68, 214428 (2003)
K. Hida, M. Shino, W. Chen, J. Phys. Soc. Jpn 73, 1587 (2004)
T. Vekua, G.I. Japaridze, H.-J. Mikeska, Phys. Rev. B 70, 014425 (2004)
G. Chaboussant, P.A. Growell, P.L. Lèvy, O. Piovesana, A. Madouri, D. Mailly, Phys. Rev. B 55, 3046 (1997)
G. Chaboussant, M.-H. Julien, Y. Fagot-Revurat, M. Hanson, P.L. Lèvy, C. Berthier, M. Horvatic, O. Piovesana, Eur. Phys. J. B 6, 167 (1998)
G. Chaboussant, Y. Fagot-Revurat, M.-H. Julien, M.E. Hanson, C. Berthier, M. Horvatic, P.L. Lèvy, O. Piovesana, Phys. Rev. Lett. 80, 2713 (1998)
D. Arcon, A. Lappas, S. Margadonna, K. Prassides, E. Ribera, J. Veciana, C. Rovira, R.T. Henriques, M. Almeida, Phys. Rev. B 60, 4191 (1999)
H. Mayaffre, H. Horvatic, C. Berthier, M.-H. Julien, P. Söransan, P.L. Lèvy, O. Piovesana, Phys. Rev. Lett. 85, 4795 (2000)
B.C. Watson, V.N. Kotov, N.W. Meisel, D.W. Hall, G.E. Granroth, W.T. Montfrooij, S.E. Nagler, D.A. Jensen, R. Backov, M.A. Petruska, G.E. Fanucci, D.R. Talham, Phys. Rev. Lett. 86, 5168 (2001)
G.I. Japaridze, P. Pogosyan, J. Phys.: Condens. Matter 18, 92971 (2006)
T. Vekua, G.I. Japaridze, H.-J. Mikeska, Phys. Rev. B 67, 064419 (2003)
G.I. Japaridze, A. Langari, S. Mahdavifar, J. Phys.: Condens. Matter 19, 076201 (2007)
A. Tribedi, I. Bose, Phys. Rev. A 79, 012331 (2009)
H.F. Song, N. Laflorencie, S. Rachel, K. Le Hur, Phys. Rev. B 83, 224410 (2011)
G.I. Japaridze, S. Mahdavifar, Eur. Phys. J. B 68, 59 (2009)
W.K. Wooters, Phys. Rev. Lett. 80, 2245 (1998)
L. Amico, R. Fazio, A. Osterloh, V. Vedal, Rev. Mod. Phys. 80, 517 (2008)
C. Lanczos, J. Res. Natl. Bur. Stand. 45, 255 (1950)
G. Grosso, L. Martinelli, G.P. Parravicini, Phys. Rev. B 51, 13033 (1995)
S. Mahdavifar, A. Akbari, J. Phys. Soc. Jpn 77, 024710 (2008)
M. Srednicki, Phys. Rev. Lett. 71, 666 (1993)
A.B. Kallin, I. Gonzales, M.B. Hastings, R.G. Melko, Phys. Rev. Lett. 103, 117203 (2009)
D. Poilblanc, Phys. Rev. Lett. 105, 077202 (2010)
F. Alet, S. Capponi, N. Laflorencie, M. Mambrini, Phys. Rev. Lett. 99, 117204 (2007)
R.W. Chhajlany, P. Tomezak, A. Wojeik, Phys. Rev. Lett. 99, 167204 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nemati, S., Batebi, S. & Mahdavifar, S. Concurrence and entanglement entropy in a dimerised spin-1/2 two-leg ladder. Eur. Phys. J. B 83, 329 (2011). https://doi.org/10.1140/epjb/e2011-20412-7
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2011-20412-7