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Survival Probability of the Néel State in Clean and Disordered Systems: An Overview

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Abstract

In this work we provide an overview of our recent results about the quench dynamics of one-dimensional many-body quantum systems described by spin-1/2 models. To illustrate those general results, here we employ a particular and experimentally accessible initial state, namely the Néel state. Both cases are considered: clean chains without any disorder and disordered systems with static random on-site magnetic fields. The quantity used for the analysis is the probability for finding the initial state later in time, the so-called survival probability. At short times, the survival probability may decay faster than exponentially, Gaussian behaviors and even the limit established by the energy-time uncertainty relation are displayed. The dynamics at long times slows down significantly and shows a powerlaw behavior. For both scenarios, we provide analytical expressions that agree very well with our numerical results.

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Acknowledgments

This work was motivated by a presentation given by one of the authors at the Workshop: Quantum Information and Thermodynamics held in São Carlos in February, 2015. This work was supported by the NSF grant No. DMR-1147430. E.J.T.H. acknowledges support from CONACyT, Mexico. LFS thanks the ITAMP hospitality, where part of this work was done.

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Authors and Affiliations

  1. Instituto de Física, Universidad Autónoma de Puebla, Apt. Postal J48, Puebla, Puebla, 72570, Mexico

    E. J. Torres-Herrera

  2. Department of Physics, Yeshiva University, New York, NY, 10016, USA

    Marco Távora & Lea F. Santos

  3. ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, 02138, USA

    Lea F. Santos

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  1. E. J. Torres-Herrera
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  2. Marco Távora
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Correspondence to Lea F. Santos.

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Torres-Herrera, E.J., Távora, M. & Santos, L.F. Survival Probability of the Néel State in Clean and Disordered Systems: An Overview. Braz J Phys 46, 239–247 (2016). https://doi.org/10.1007/s13538-015-0366-3

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