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Replica symmetry breaking in spin glasses in the replica-free Keldysh formalism
by Johannes Lang, Subir Sachdev, Sebastian Diehl
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Johannes Lang · Subir Sachdev |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202406_00046v2 (pdf) |
| Date accepted: | 2024-11-07 |
| Date submitted: | 2024-09-04 22:38 |
| Submitted by: | Lang, Johannes |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We show that the algebra of Parisi ultrametric matrices is recovered by the real-time, replica-free, Dyson-Keldysh equations of infinite-range quantum spin glasses in the late time glassy limit. This connects to earlier results on classical and quantum systems showing how ultrametricity emerges from the persistent slow aging dynamics of the glass phase. The stationary spin glass state thereby spontaneously breaks thermal symmetry, or the Kubo-Martin-Schwinger relation of a state in global thermal equilibrium. We describe the Keldysh path integral of the infinite-range Ising model in transverse and longitudinal fields, and in the context of the Landau expansion of the action functional, show how the long-time limit connects to the full replica symmetry breaking obtained in the equilibrium formalism. We also illustrate our formalism by applying it to the spherical quantum $p$-spin model, which only exhibits one-step replica symmetry breaking
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
List of changes
Clarified novelty of results and relation to previous work in abstract and Sec. 1
Significantly extended the list of references to more accurately represent the current state of the field
Extended Sec. 2.2 to increase the accessibility of Keldysh formalism used in the manuscript and clarify the physical protocol.
Numerous changes to notation and phrasing to enhance readability
Published as SciPost Phys. 17, 160 (2024)
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Dear Editor,
I have read the new version of this manuscript as well as the Author response. I am glad to see that the Authors have followed the comments by the two Referees and largely revised their manuscript. It is now more clear how to place this work in the literature on classical and quantum spin glasses and what are the major novelties. Although one could argue that this work lacks major groundbreaking new results and that to a certain extent most of its content was known to the community (at least on the classical side), I still believe there is a benefit in presenting the material as it is done in this work for quantum spin glasses. Overall I think the manuscript can be accepted for publication, even though SciPost Physics more restrictive acceptance criteria, as opposed to SciPost Core, do not seem to be fully met here.
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Publish (meets expectations and criteria for this Journal)