SciPost Submission Page
Topologically ordered steady states in open quantum systems
by Zijian Wang, Xu-Dong Dai, He-Ran Wang, Zhong Wang
This Submission thread is now published as
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: |
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| 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
Published as SciPost Phys. 17, 167 (2024)
Reports on this Submission
Report #2 by Anonymous (Referee 1) on 2024-11-5 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202409_00013v1, delivered 2024-11-04, doi: 10.21468/SciPost.Report.10040
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)
Report #1 by Anonymous (Referee 2) on 2024-11-2 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202409_00013v1, delivered 2024-11-02, doi: 10.21468/SciPost.Report.10029
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%)