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Logarithmic, noise-induced dynamics in the Anderson insulator

by Talía Lezama Mergold Love, Yevgeny Bar Lev

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Submission summary

Authors (as registered SciPost users): Yevgeny Bar Lev · Talía L. M. Lezama
Submission information
Preprint Link: scipost_202201_00002v1  (pdf)
Date accepted: 2022-05-04
Date submitted: 2022-01-06 21:47
Submitted by: L. M. Lezama, Talía
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approaches: Theoretical, Computational


We study the dynamical behavior of the one-dimensional Anderson insulator in the presence of a local noise. We show that the noise induces logarithmically slow energy and entanglement growth, until the system reaches an infinite-temperature state, where both quantities saturate to extensive values. The saturation value of the entanglement entropy approaches the average entanglement entropy over all possible product states. At infinite temperature, we find that a density excitation spreads logarithmically with time, without any signs of asymptotic diffusive behavior. In addition, we provide a theoretical picture which qualitatively reproduces the phenomenology of particle transport.

Published as SciPost Phys. 12, 174 (2022)

List of changes

1) Emphasized in the abstract the one-dimensional nature of the model.
2) Added a sentence in Secs. I and V regarding experimental setups that could be used to confirm our theoretical results, as well as new references [35-37].
3) Defined precisely the noise distribution.
4) Added details on the accuracy of the method at the end of Sec. II.
5) Defined the single-particle eigenstates earlier (below Eq. (14)), as well as specified that these are ordered by energy in Eq. (14) to obtain the ground state single-particle density matrix.
6) Corrected typos in the average symbols.
7) Improved the first paragraph of Sec. III (B) and added a discussion of the implications of the entanglement entropy scaling at the end of the same subsection.
8) Added a new panel to Fig. 2 showing results on the entanglement profile and related discussion at the end of Sec. III (B)
9) Corrected typo in Eq. (21)
10) Improved the figures and captions.

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