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Topologically ordered steady states in open quantum systems

by Zijian Wang, Xu-Dong Dai, He-Ran Wang, Zhong Wang

Submission summary

Authors (as registered SciPost users): Heran Wang · Zijian Wang
Submission information
Preprint Link: scipost_202409_00013v1  (pdf)
Date accepted: 2024-11-13
Date submitted: 2024-09-11 15:37
Submitted by: Wang, Zijian
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical

Abstract

The interplay between dissipation and correlation can lead to novel emergent phenomena in open systems. Here we investigate ``steady-state topological order'' defined by the robust topological degeneracy of steady states, which is a generalization of the ground-state topological degeneracy of closed systems. Specifically, we construct two representative Liouvillians using engineered dissipation, and exactly solve the steady states with topological degeneracy. We find that while the steady-state topological degeneracy is fragile under noise in two dimensions, it is stable in three dimensions, where a genuine many-body phase with topological degeneracy is realized. We identify universal features of steady-state topological physics such as the deconfined emergent gauge field and slow relaxation dynamics of topological defects. The transition from a topologically ordered phase to a trivial phase is also investigated via numerical simulation. Our work highlights the essential difference between ground-state topological order in closed systems and steady-state topological order in open systems.

Author indications on fulfilling journal expectations

  • Provide a novel and synergetic link between different research areas.
  • Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
  • Detail a groundbreaking theoretical/experimental/computational discovery
  • Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Accepted in target Journal

Editorial decision: For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)


Reports on this Submission

Report #2 by Anonymous (Referee 1) on 2024-11-5 (Invited Report)

Report

This study explores solvable models of steady-state topological orders, examining their stability under perturbations and analyzing both confinement transitions and relaxation dynamics. The results are substantial, comprehensive, and well-grounded, making a strong case for publication in SciPost.

I have a minor question regarding the characterization of topological order in mixed states through higher-form symmetry breaking, which may be either strong or weak depending on the conditions. Specifically, the authors observe that while steady-state topological degeneracy is susceptible to noise in two dimensions, it remains stable in three dimensions, where a true many-body phase with topological degeneracy emerges. Could a Mermin-Wagner-type argument, based on higher-form symmetry and dimensionality, provide insight into which dimensions and d-form symmetry breakings (for mixed-state topological order) yield stability?

Recommendation

Publish (meets expectations and criteria for this Journal)

  • validity: -
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Report #1 by Anonymous (Referee 2) on 2024-11-2 (Invited Report)

Report

This work studied solvable models of steady-state topological orders, investigated their stability under perturbations, and also discussed confinement transition as well as relaxation properties. The result is significant, complete, and solid. I strongly recommend publishing this article in SciPost Physics.

I am curious about one question that I hope the authors could address. In the discussion of confinement and deconfinement, the authors use the expectation values of Wilson loops as a diagnostic. In conventional Lorentz invariant field theories, Wilson loop vacuum expectation values are related to the interaction strength between gauge charges via a Euclidean spacetime rotation, and thus indicates confinement/deconfinement (defined as whether gauge charges have long-range interactions or not). In Lindbladian dynamics as studied in this work, is there still a similar Lorentz invariance argument? If not, would it be possible to find some energetic evidence of confinement-deconfinement transition in this particular example? Maybe this is related to the subsequent relaxation time result.

I have also spotted a typo. When introducing the vectorized density matrix in the double Hilbert space (second paragraph of Section 3), there is an extra summation symbol $\sum_{mn}$.

Recommendation

Publish (easily meets expectations and criteria for this Journal; among top 50%)

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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