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Parity effects and universal terms of O(1) in the entanglement near a boundary

by Henning Schloemer, Chunyu Tan, Stephan Haas, Hubert Saleur

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Submission summary

Authors (as registered SciPost users): Henning Schloemer
Submission information
Preprint Link: scipost_202207_00018v2  (pdf)
Date accepted: 2022-09-27
Date submitted: 2022-09-22 20:27
Submitted by: Schloemer, Henning
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Quantum Physics
Approaches: Theoretical, Computational


In the presence of boundaries, the entanglement entropy in lattice models is known to exhibit oscillations with the (parity of the) length of the subsystem, which however decay to zero with increasing distance from the edge. We point out in this article that, when the subsystem starts at the boundary and ends at an impurity, oscillations of the entanglement (as well as of charge fluctuations) appear which do not decay with distance, and which exhibit universal features. We study these oscillations in detail for the case of the XX chain with one modified link (a conformal defect) or two successive modified links (a relevant defect), both numerically and analytically. We then generalize our analysis to the case of extended (conformal) impurities, which we interpret as SSH models coupled to metallic leads. In this context, the parity effects can be interpreted in terms of the existence of non-trivial topological phases.

Author comments upon resubmission

We would like to thank all three referees for their careful reading and helpful suggestions for improving the manuscript. Below is a collection of responses addressing the raised remarks by the referees.

Referee 1:
We have added additional comments to the analytical discussion, which hopefully clarify some subtleties and improve the overall readability of the section.

Referee 2:
We slightly reformulated our conjecture, hopefully clarifying the discussion of the universality of terms of O(1).

In Chapter 4, we have pointed out that entanglement entropy differences in the full SSH model share similarities with the case of an extended alternating impurity as well as a single modified bond. Though the underlying models are fundamentally different (i.e. while the SSH model is gapped and features a topologically non-trivial phase, the impurity system is gapless), we consider the resemblance of the terms of O(1) in topological and closely related non-topological models to be an intriguing open possibility for further investigations.

Referee 3:
We agree with the referee that the valence bond picture does not capture the exact nature of the ground state. Nevertheless, it yields an intuitive platform to understand the entanglement entropy differences in the limit of weak and strong impurities, which we have clarified in the revised manuscript.

Lastly, we thank all referees for pointing out various typos, notation inconsistencies and literature suggestions, which we have addressed in the revised version.

Published as SciPost Phys. 13, 110 (2022)

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