Abstract
We examine the dynamics of nearest-neighbor bipartite concurrence and total correlations in the spin-1/2 XXZ model with random fields. We show, starting from factorized random initial states, that the concurrence can suffer entanglement sudden death in the long time limit and therefore may not be a useful indicator of the properties of the system. In contrast, we show that the total correlations capture the dynamics more succinctly, and further reveal a fundamental difference in the dynamics governed by the ergodic versus many-body localized phases, with the latter exhibiting dynamical oscillations. Finally, we consider an initial state composed of several singlet pairs and show that by fixing the correlation properties, while the dynamics do not reveal noticeable differences between the phases, the long-time values of the correlation measures appear to indicate the critical region.
Graphical abstract
Article PDF
Similar content being viewed by others
References
A. Osterloh, L. Amico, G. Falci, R. Fazio, Nature 416, 608 (2002)
T.J. Osborne, M.A. Nielsen, Phys. Rev. A 66, 032110 (2002)
L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517 (2008)
L. Amico, A. Osterloh, F. Plastina, R. Fazio, G. Massimo Palma, Phys. Rev. A 69, 022304 (2004)
P. Calabrese, J. Cardy, J. Stat. Mech. Theor. Exp. 04010 (2005)
G. De Chiara, S. Montangero, P. Calabrese, R. Fazio, J. Stat. Mech. Theor. Exp. P03001 (2006)
D. Basko, I. Aleiner, B. Altshuler, Ann. Phys. 321, 1126 (2006)
R. Nandkishore, D.A. Huse, Annu. Rev. Condens. Matter Phys. 6, 15 (2015)
R. Vasseur, J.E. Moore, J. Stat. Mech. Theor. Exp. 064010 (2016)
N. Laflorencie, Phys. Rep. 646, 1 (2016)
M. Serbyn, Z. Papić, D.A. Abanin, Phys. Rev. Lett. 111, 127201 (2013)
M. Serbyn, M. Knap, S. Gopalakrishnan, Z. Papić, N.Y. Yao, C.R. Laumann, D.A. Abanin, M.D. Lukin, E.A. Demler, Phys. Rev. Lett. 113, 147204 (2014)
M. Serbyn, Z. Papić, D.A. Abanin, Phys. Rev. B 90, 174302 (2014)
D.A. Huse, R. Nandkishore, V. Oganesyan, Phys. Rev. B 90, 174202 (2014)
G. De Tomasi, S. Bera, J.H. Bardarson, F. Pollman, Phys. Rev. Lett. 118, 016804 (2017)
S. Bera, A. Lakshminarayan, Phys. Rev. B 93, 134204 (2016)
J. Goold, C. Gogolin, S.R. Clark, J. Eisert, A. Scardicchio, A. Silva, Phys. Rev. B 92, 180202 (2015)
J.L.C. da C. Filho, A. Saguia, L.F. Santos, M.S. Sarandy, arXiv:1705.01957
M. Schreiber, S.S. Hodgman, P. Bordia, H.P. Lüschen, M.H. Fischer, R. Vosk, E. Altman, U. Schneider, I. Bloch, Science 349, 842 (2015)
S.S. Kondov, W.R. McGehee, W. Xu, B. DeMarco, Phys. Rev. Lett. 114, 083002 (2015)
J.-Y. Choi, S. Hild, J. Zeiher, P. Schauß, A. Rubio-Abadal, T. Yefsah, V. Khemani, D.A. Huse, I. Bloch, C. Gross, Science 352, 1547 (2016)
J. Smith, A. Lee, P. Richerme, B. Neyenhuis, P.W. Hess, P. Hauke, M. Heyl, D.A. Huse, C. Monroe, Nat. Phys. 12, 907 (2016)
A. Nanduri, H. Kim, D.A. Huse, Phys. Rev. B 90, 064201 (2014)
D.J. Luitz, N. Laflorencie, F. Alet, Phys. Rev. B 91, 081103 (2015)
T. Enss, F. Andraschko, J. Sirker, Phys. Rev. B 95, 045121 (2017)
A. De Luca, B.L. Altshuler, V.E. Kravtsov, A. Scardicchio, Phys. Rev. Lett. 113, 046806 (2014)
V. Khemani, D.N. Sheng, D.A. Huse, arXiv:1702.03932
T. Yu, J.H. Eberly, Science 323, 598 (2009)
R. Vosk, D.A. Huse, E. Altman, Phys. Rev. X 5, 031032 (2015)
F. Iemini, A. Russomanno, D. Rossini, A. Scardicchio, R. Fazio, Phys. Rev. B 94, 214206 (2016)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Campbell, S., Power, M.J.M. & De Chiara, G. Dynamics and asymptotics of correlations in a many-body localized system. Eur. Phys. J. D 71, 206 (2017). https://doi.org/10.1140/epjd/e2017-80302-8
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjd/e2017-80302-8