SciPost Submission Page
Operator entanglement in $\mathrm{SU}(2)$-symmetric dissipative quantum many-body dynamics
by Lin Zhang
Submission summary
| Authors (as registered SciPost users): | Lin Zhang |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2410.18468v1 (pdf) |
| Date submitted: | 2024-11-04 23:57 |
| Submitted by: | Zhang, Lin |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
The presence of symmetries can lead to nontrivial dynamics of operator entanglement in open quantum many-body systems, which characterizes the cost of an matrix product operator (MPO) representation of the density matrix and provides a measure for the classical simulability. One example is the $\mathrm{U}(1)$-symmetric open quantum systems with dephasing, in which the operator entanglement increases logarithmically at late times instead of being suppressed by the dephasing. Here we numerically study the far-from-equilibrium dynamics of operator entanglement in a dissipative quantum many-body system with the more complicated $\mathrm{SU}(2)$ symmetry and dissipations beyond dephasing. We show that after the initial rise and fall, the operator entanglement also increases again in a logarithmic manner at late times in the $\mathrm{SU}(2)$-symmetric case. We find that this behavior can be fully understood from the corresponding $\mathrm{U}(1)$ subsymmetry by considering the symmetry-resolved operator entanglement. But unlike the $\mathrm{U}(1)$-symmetric case with dephasing, both the classical Shannon entropy associated with the probabilities for the half system being in different symmetry sectors and the corresponding symmetry-resolved operator entanglement have nontrivial contributions to the late time logarithmic growth of operator entanglement. Our results show evidence that the logarithmic growth of operator entanglement at long times is a generic behavior of dissipative quantum many-body dynamics with $\mathrm{U}(1)$ as the symmetry or subsymmetry and for more broad dissipations beyond dephasing. We show that the latter is valid even for open quantum systems with only $\mathrm{U}(1)$ symmetry by breaking the $\mathrm{SU}(2)$ symmetry of our quantum dynamics to $\mathrm{U}(1)$.
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
Current status:
Reports on this Submission
Strengths
1- Analyzing operator entanglement growth in this specific dissipative model with SU(2) symmetry is new.
2- The presentation of the results is clear and the manuscript is well written.
Weaknesses
1- The manuscript provides interesting new numerical evidence for a specific model, but no new analytical or universal understanding is achieved.
2- To judge the validity of the results a discussion on details of potential numerical errors for the data is missing. Convergence plots are missing.
Report
In this manuscript the author analyzes the long-time growth of operator entanglement in a dissipative spin-chain with SU(2) symmetry. This follows up earlier works with U(1) symmetric models, where a universal log-growth behavior was attributed to the classical entropy growth stemming from symmetry block diffusion. Here, new numerical evidence suggests that also in this specific SU(2) symmetric setup, the U(1) subsymmetry leads to log-growth behavior.
Almost all general acceptance criteria are fulfilled:
1- The paper is well written and results are clearly presented (only minor suggestions).
2- Details on all physical and numerical parameters are clear.
3- Relevant literature is properly cited.
4- The conclusion is written well and results are objectively summarized
5- The introduction to the problem is well done.
6- Some more details on the numerical convergence behavior are missing and convergence plots should be provided.
While the results are certainly an interesting addition to the existing knowledge, unfortunately I don't agree with the author on the claimed expectations for SciPost Physics being fulfilled:
1- This work is focused on a sub-field of entanglement dynamics in open quantum spin-chains. I fail to see any synergetic link between research areas.
2- As honestly described in the manuscript, the numerical calculations lead to some follow-up insight, amending previous understanding. I don't see it opening up a new research direction. While further investigations, including e.g. SU(N>2) or SO(N) symmetries would indeed be interesting, they would not be multi-pronged, and not be a consequence of this numerical paper.
3- While being interesting, I don't find the findings ground-breaking. As the author honestly writes, this work provides new numerical evidence on operator entanglement growth being a generic feature of U(1). However, this conjecture is not new, and also the paper does not add any new analytical ground-breaking understanding on setups with additional symmetries.
Overall, I therefore think that after some revisions (see below), this paper is publishable, but not in SciPost Physics. All criteria for SciPost Physics Core are fulfilled, so the paper could be published there.
Requested changes
1- Convergence plots need to be shown and a discussion on potential numerical errors/artifacts needs to be added. For example, in Fig. 1(d) results for $\gamma=0.05J$ and $\gamma=0.1J$ exhibit strange wiggles. Is this due to: Fitting problems over finite time? Time-step in the simulations? Finite bond-dimension? The 4-th order Trotter decomposition usually allows to use large time-steps, but the reader should be convinced about the convergence of the results in the time-step and in the bond-dimension by showing some convergence plots in an appendix.
2- (minor) I find some wording in the introduction of the paper a bit "over-the-top". I suggest to remove words like "fantastic", "extremely".
3- Also some statements are a bit imprecise. For example, I would not call operator entanglement a "measure" for classical simulability (strictly speaking, low von Neumann entanglement entropy does e.g. not guarantee an efficient classical state representation [24]). Furthermore, fast operator entanglement growth make simulations with matrix product density operators hard, but not necessarily with another numerical technique. Lastly, I would suggest to use the acronym MPDO (matrix product density operator) instead of MPO, as the latter is more commonly used in a general context and for Hamiltonian representations.
Recommendation
Accept in alternative Journal (see Report)