SciPost Submission Page
Bypassing eigenstate thermalization with experimentally accessible quantum dynamics
by Amit Vikram
Submission summary
| Authors (as registered SciPost users): | Amit Vikram |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202509_00047v1 (pdf) |
| Date submitted: | Sept. 26, 2025, 4:37 a.m. |
| Submitted by: | Amit Vikram |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Eigenstate thermalization has played a prominent role as a determiner of the validity of quantum statistical mechanics since von Neumann's early works on quantum ergodicity. However, its connection to the dynamical process of quantum thermalization relies sensitively on nondegeneracy properties of the energy spectrum, as well as detailed features of individual eigenstates that are effective only over correspondingly large timescales, rendering it generically inaccessible given practical timescales and finite experimental resources. Here, we introduce the notion of energy-band thermalization to address these limitations, by coarse-graining over energy level spacings with a finite energy resolution. We show that energy-band thermalization implies the thermalization of an observable in almost all states (in any orthonormal basis) over accessible timescales without relying on microscopic properties of the energy eigenvalues or eigenstates, and conversely, can be efficiently accessed in experiments via the dynamics of a single mixed state (for a given observable) with only polynomially many resources in the system size. This allows us to directly determine thermalization, including in the presence of conserved charges, from this state: Most strikingly, if an observable thermalizes in this initial state over a finite range of times, then it must thermalize in almost all physical initial states over all longer timescales. As applications, we derive a finite-time Mazur-Suzuki inequality for quantum transport with approximately conserved charges, and establish the thermalization of local observables over finite timescales in almost all accessible states in (generally inhomogeneous) dual-unitary quantum circuits. We also propose measurement protocols for general many-qubit systems. This work initiates a rigorous treatment of quantum thermalization in terms of experimentally accessible quantities.
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- Fundamental contribution to the field of thermalization 2- Focus on physically accessible quantities 3- Rigorous work
Weaknesses
1- Mostly catering to experts in the field 2- Physical meaning and intuition could be clearer
Report
This work addresses the important problem of thermalization of isolated quantum systems. The main motivation stems from the fact that the standard picture invoking the eigenstate thermalization hypothesis relies on eigenpairs of quantum many-body systems, which per se cannot be prepared in experiments. The idea behind this paper is that the conditions that ETH poses may be relaxed, keeping thermalization but with less strict conditions on the mathematical structure of the eigenstates. This is achieved by a sort of coarse graining procedure, which focuses on energy bands instead of individual eigenstates. The author shows that this also allows the consideration of systems with degenerate spectra. The main point is to avoid the notion of any quantity which is experimentally inaccessible: infinite times, infinite time resolution, infinite energy resolution. This is conceptually a very important point, and appears to relax the conditions for thermalization with respect to standard ETH.
This paper is a comprehensive and rigorous contribution to the field and I recommend publication. I would like to point out that it is relatively dense material and difficult to access for a broader audience. The discussion is on an abstract level and would perhaps profit from a few more examples, which might be mentioned in the summary of results to make this a bit more accessible. In particular, I was wondering for which systems these relaxed conditions compared to ETH are actually relevant. Which model systems do not satisfy ETH but still thermalize under energy band thermalization? Another question which came to my mind was the behavior of systems with quantum many-body scars (e.g. the PXP model cf. for example Turner et al. Phys. Rev. B 98, 155134 DOI: https://doi.org/10.1103/PhysRevB.98.155134). In this system, ETH is not strictly satisfied, since there are (some) eigenstates which have low entanglement in the vicinity of highly entangled (ETH) thermal states. Does this system show energy-band thermalization since the ETH states overwhelm the nonthermal scar states? On the other hand, we know that some initial states do not reach equilibrium, so there must be exceptions which apply here. It would be interesting to understand this in the author's framework.
As far as I can see, the offdiagonal aspect of ETH does not play a role here. Can the framework be extended to include this, i.e. to the full thermalization dynamics?
Tiny technical comments:
- The author points out that some observables never thermalize (e.g. projectors to eigenstates). There is an interesting relevant paper classifying such observables here: Khaymovich, Haque and McClarty, Phys. Rev. Lett. 122, 070601 (2019) DOI: https://doi.org/10.1103/PhysRevLett.122.070601
- line 186: "any level spacing" -> "any inverse level spacing"
- line 323: "arbtirary" -> "arbitrary"
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Report #1 by Anonymous (Referee 1) on 2025-12-25 (Invited Report)
The referee discloses that the following generative AI tools have been used in the preparation of this report:
I use chat GPT for correcting typo for the reports. I stress that I do not use AI for giving technical contents.
Strengths
1)
In particular, the notion of energy-band thermalization discussed in Section~5 provides a nice resolution to subtleties that many papers typically dismiss by assumption for simplicity.
2)
The discussion in Section~6 offers a robust clarification of finite-time thermalization. To my knowledge, this point has not been discussed clearly in the existing literature.
3)
I have checked the derivations of the inequalities, and they appear to be mathematically correct.
Weaknesses
1)
Although the authors aim to address realistic situations, they do not discuss cases involving multiple observables that may not commute with each other.
2)
In several places, the authors refer to a ``physical basis.'' However, the meaning of this term is unclear to me. In realistic situations, and even from a theoretical perspective, one generally considers superpositions of such bases.
Report
Requested changes
I add the pdf file which including comments and request for revision.
Recommendation
Publish (meets expectations and criteria for this Journal)