SciPost logo

SciPost Submission Page

Strong Hilbert space fragmentation via emergent quantum drums in two dimensions

by Anwesha Chattopadhyay, Bhaskar Mukherjee, K. Sengupta, Arnab Sen

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Arnab Sen · Krishnendu Sengupta
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-04-06
Date submitted: 2023-01-26 05:02
Submitted by: Sen, Arnab
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approaches: Theoretical, Computational


We introduce a disorder-free model of $S=1/2$ spins on the square lattice in a constrained Hilbert space where two up-spins are not allowed simultaneously on any two neighboring sites of the lattice. The interactions are given by ring-exchange terms on elementary plaquettes that conserve both the total magnetization as well as dipole moment. We show that this model provides a tractable example of strong Hilbert space fragmentation in two dimensions with typical initial states evading thermalization with respect to the full Hilbert space. Given any product state, the system can be decomposed into disjoint spatial regions made of edge and/or vertex sharing plaquettes that we dub as "quantum drums". These quantum drums come in many shapes and sizes and specifying the plaquettes that belong to a drum fixes its spectrum. The spectra of some small drums is calculated analytically. We study two bigger quasi-one-dimensional drums numerically, dubbed "wire" and a "junction of two wires" respectively. We find that these possess a chaotic spectrum but also support distinct families of quantum many-body scars that cause periodic revivals from different initial states. The wire is shown to be equivalent to the one-dimensional PXP chain with open boundaries, a paradigmatic model for quantum many-body scarring; while the junction of two wires represents a distinct constrained model.

Author comments upon resubmission

Dear Editor,

Thanks for sending us the referee comments and also the comments by an anonymous commenter. The questions and comments were very useful and helped us improve the presentation of the paper and also remove some points of confusion. We have now responded to all the comments from both referees and the anonymous commenter (in the form of a reply to their individual reports) and hope that you would find the present version to be publishable in SciPost

With best regards,

Anwesha Chattopadhyay, Bhaskar Mukherjee, K. Sengupta, Arnab Sen

List of changes

1. Changed a phrase in the Abstract.

2. Added a sentence to the introduction on the suggestion of the anonymous commenter.

3. Added a couple of phrases to the introduction to clarify a few points that the referees had found confusing.

4. Added a phrase and a paragraph to Section 2 (before the beginning of Section 2.1) on the suggestion of the anonymous commenter.

5. Section 2.1.2 has been rewritten a bit to clarify a point raised by the anonymous commenter.

6. Section 2.2 has been shortened a bit and the notation simplified on the suggestion of the anonymous commenter.

7. The earlier Section 3.2 titled "Wire decomposition of quantum drums" has now been moved to Section 2.4 which consists of two subsections titled Sec. 2.4.1 "Calculating fragment dimension from wire decomposition" and Section 2.4.2 "Constructing entire drums from wire-decomposed reference states". This rearrangement and some clarifying remarks here should make it easier to follow some of the analytic arguments.

8. Some clarifying remarks have been added in Section 3 to make the analytic arguments for strong Hilbert space fragmentation more explicit after receiving the referee reports. We have also changed the title of Sec. 3.3 to
"Large Krylov subspaces and absence of ETH-predicted thermalization" from Absence of thermalization from typical product states" (Sec. 3.4 of the previous version).

9. An analytic prediction in the form of a dotted curve has been added to Fig. 11 (right panel).

10. A new schematic figure (Fig. 15) has been added to summarize the fate of a typical initial state as a function of up-spins (bosons), $n$.

11. Added a couple of sentences in the section: Discussion to highlight a few points mentioned by the referees.

Published as SciPost Phys. 14, 146 (2023)

Reports on this Submission

Anonymous Report 2 on 2023-1-30 (Invited Report)


The authors have addressed my remarks and I recommend publication.

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

Anonymous Report 1 on 2023-1-26 (Invited Report)


I have reviewed the revised version, and my concerns have been addressed. I can recommend publication in scipost.

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

Login to report or comment