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Hierarchy of degenerate stationary states in a boundary-driven dipole-conserving spin chain
by Apoorv Srivastava, Shovan Dutta
Submission summary
| Authors (as registered SciPost users): | Shovan Dutta · Apoorv Srivastava |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2411.03309v1 (pdf) |
| Date submitted: | 2024-11-12 07:31 |
| Submitted by: | Dutta, Shovan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Kinetically constrained spin chains serve as a prototype for structured ergodicity breaking in isolated quantum systems. We show that such a system exhibits a hierarchy of degenerate steady states when driven by incoherent pump and loss at the boundary. By tuning the relative pump and loss and how local the constraints are, one can stabilize mixed steady states, noiseless subsystems, and various decoherence-free subspaces, all of which preserve large amounts of information. We also find that a dipole-conserving bulk suppresses current in steady state. These exact results based on the flow in Hilbert space hold regardless of the specific Hamiltonian or drive mechanism. Our findings show that a competition of kinetic constraints and local drives can induce different forms of ergodicity breaking in open systems, which should be accessible in quantum simulators.
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Report
The authors investigate how kinetic constraints in boundary driven dipole-conserving spin chains can produce a hierarchy of degenerate stationary states that break ergodicity, in contrast to conventional boundary driven spin chains which generically reach a unique steady state. By analysing both fragmented and unfragmented cases under different driving regimes (unipolar and bipolar), they demonstrate how decoherence-free subspaces can be stabilized even in the presence of symmetry-breaking drives. The results are exact, based on the symmetry and structure of the Hamiltonian rather than specific forms of dynamics. The paper is clear and well written, timely adding valuable insights into ergodicity-breaking phenomena in open quantum systems, relevant to fields such as quantum thermodynamics and quantum error correction. With some minor corrections which I will elaborate on below, I believe the work should be published.
1. It would be helpful for the reader if the values of N_DFS, N_sector and d_DFS were derived in an appendix. I appreciate they may be simple derivations, but I still think it's worth including.
2. What's the intuition behind the root configurations given in section 3? Once given, they can be understood but I'm curious as to how the authors arrived at them.
3. Unless I’ve misunderstood, the statement that sequences of 3 or more consecutive 1's or 0's do not evolve under the Hamiltonian is incorrect. For example, the state 111001 can evolve to 110110, 1000110 can evolve to 1001001 etc. I understand that the sequence in isolation can’t evolve, but this isn’t quite what is stated.
4. The statement that any state beginning with 111 and ending in 000 is unaffected by the drives is true and intuitive but not immediately obvious. The reasoning given for which states to discard (Eq's 10 and 11) could be used to explain this but is given after the statement, so needs some slight restructuring. The same goes for the discussion about shielding the bulk with 111 and 000.
5. “By varying whether the dipole conservation is local or global", this statement is incorrect. In both cases of the allowed separation for the hops, the dipole moment is conserved. The allowed hop separation is what changes from local to global, which controls the fragmentation.
6. In the first row of Figure 1, arrows to the right denote losses and arrows to the left denote pumping. Why is this switched for rows 2 and 3?
Recommendation
Ask for minor revision
Author: Shovan Dutta on 2024-12-20 [id 5056]
(in reply to Report 1 on 2024-12-19)We sincerely thank the Referee for the positive and timely report. We will address all of the points in our full response. For now, we would like to clarify that: (i) For the 3rd point, the statement is indeed not correctly stated in the manuscript. It should say that "any state composed solely of sequences of three or more 1's or 0's does not evolve under the Hamiltonian." (ii) For the 5th point, the Referee is correct that the dipole moment D is conserved in both cases. However, when the hops are adjacent, D is also conserved locally (in the same sense as used in Ref. [14]; see also Refs. [12, 15]), which gives subdiffusion, whereas for large separation, D is only conserved globally, which gives diffusion [14, 15]. We will improve this wording in the manuscript.