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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

Submission summary

As Contributors: Alexey Khudorozhkov · Apoorv Tiwari
Arxiv Link: (pdf)
Date accepted: 2022-05-20
Date submitted: 2022-05-12 04:21
Submitted by: Khudorozhkov, Alexey
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational


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.

Current status:
Publication decision taken: accept

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

Author comments upon resubmission

We address the concern raised by one of the referees about the existence of emergent local conserved quantities in the considered model. We have added Appendix H, where we present an analytical proof that the XY-plaquette model does not have any local conserved operators.

List of changes

- Added Appendix H, where we prove that local conserved quantities do not exist in the XY-plaquette model.

Reports on this Submission

Anonymous Report 1 on 2022-5-13 (Invited Report)


The authors have now clearly demonstrated their system has true fragmentation and I judge the main conclusion of the paper to be correct.

As I wrote in my first report the paper deals with an extensive study of a topical subject and the model studied is a nice addition to the quickly growing zoo of models with Hilbert space fragmentation. In this case the interplay between subsystem symmetries and fragmentation leads to a "shielding" effect, which is in itself new.

However, despite this I cannot find sufficient evidence of any of the SciPost Physics acceptance criteria being fulfilled by this work:

1. Detail a groundbreaking theoretical/experimental/computational discovery;

2. Present a breakthrough on a previously-identified and long-standing research stumbling block;

3. Open a new pathway in an existing or a new research direction, with clear potential for multipronged follow-up work;

4. Provide a novel and synergetic link between different research areas.

One could possibly argue for 3, but the model studied seems quite specific and, since the authors do not discuss any experimental implementation that could realize the model, I do not see "clear potential for multipronged follow-up work".

Based on this conclusion I recommend publication in SciPost Physics Core.

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

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