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Hilbert space fragmentation in a 2D quantum spin system with subsystem symmetries
by Alexey Khudorozhkov, Apoorv Tiwari, Claudio Chamon, Titus Neupert
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Submission summary
| Authors (as registered SciPost users): | Alexey Khudorozhkov · Apoorv Tiwari |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2107.09690v3 (pdf) |
| Date submitted: | 2022-04-02 21:25 |
| Submitted by: | Khudorozhkov, Alexey |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We consider a 2D quantum spin model with ring-exchange interaction that has subsystem symmetries associated to conserved magnetization along rows and columns of a square lattice, which implies the conservation of the global dipole moment. In a certain regime, the model is non-integrable, but violates the eigenstate thermalization hypothesis through an extensive Hilbert space fragmentation, including an exponential number of inert subsectors with trivial dynamics, arising from kinetic constraints. While subsystem symmetries are quite restrictive for the dynamics, we show that they alone cannot account for such a number of inert states, even with infinite-range interactions. We present a procedure for constructing shielding structures that can separate and disentangle dynamically active regions from each other. Notably, subsystem symmetries allow the thickness of the shields to be dependent only on the interaction range rather than on the size of the active regions, unlike in the case of generic dipole-conserving systems.
Author comments upon resubmission
List of changes
1. Changed the left panel of Fig. 2. We changed the horizontal axis to N*log(N). We show that the number of symmetry sectors is proportional to N*log(N). This scaling behavior is expected for continuous subsystem symmetries, and therefore we prove that the subsystem symmetries alone are not responsible for Hilbert space fragmentation in the considered model. We added corresponding comments on this in Section II.
2. At the beginning of Section III, we added a clarification on the notation for subsystem symmetry quantum numbers.
3. In "Locality and fragmentation" subsection of Section III, in Eq. (9), we added another example of a possible interaction term that preserves subsystem symmetries. The "shape" of this interaction has intersecting edges. This example is supposed to clarify our comment on self-intersecting boundaries of the interaction "figures" below Eq. (9).
4. In Section IV, we added an important statement, that non-locality of the shields implies that in the thermodynamic limit the probability of having a shield tends to zero.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 3) on 2022-4-16 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2107.09690v3, delivered 2022-04-16, doi: 10.21468/SciPost.Report.4931
Report
The authors have made considerable efforts to check the conditions of https://arxiv.org/abs/2108.10324 for fragmentation based on commutation algebras.
However, as mentioned in my first report, as discussed in https://arxiv.org/abs/2108.13411 other local algebraic structures beyond subsystem symmetries (e.g. [H,A]=\omega A with A acting on a subsystem) can further induce fragmentation. Such a case would likewise not be "true" fragmentation and it is not clear to me from the authors expanded study whether there are such algebras in their system.
Requested changes
Check the conditions discussed above to provide further evidence that the system has true fragmentation.
Report #1 by Rahul Nandkishore (Referee 1) on 2022-4-6 (Invited Report)
Report
I think the authors have adequately addressed the reports and the manuscript can now be published.
Author: Alexey Khudorozhkov on 2022-05-12 [id 2458]
(in reply to Report 2 on 2022-04-16)We have added Appendix H, where we prove analytically that the XY-plaquette model cannot exhibit local conserved quantities. Please see the resubmition.