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Partial thermalisation of a two-state system coupled to a finite quantum bath
by Philip J. D. Crowley, Anushya Chandran
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Philip Crowley |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202106_00009v2 (pdf) |
| Date accepted: | 2022-02-22 |
| Date submitted: | 2022-01-04 23:13 |
| Submitted by: | Crowley, Philip |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
The eigenstate thermalisation hypothesis (ETH) is a statistical characterisation of eigen-energies, eigenstates and matrix elements of local operators in thermalising quantum systems. We develop an ETH-like ansatz of a partially thermalising system composed of a spin-1/2 coupled to a finite quantum bath. The spin-bath coupling is sufficiently weak that ETH does not apply, but sufficiently strong that perturbation theory fails. We calculate (i) the distribution of fidelity susceptibilities, which takes a broadly distributed form, (ii) the distribution of spin eigenstate entropies, which takes a bi-modal form, (iii) infinite time memory of spin observables, (iv) the distribution of matrix elements of local operators on the bath, which is non-Gaussian, and (v) the intermediate entropic enhancement of the bath, which interpolates smoothly between zero and the ETH value of log 2. The enhancement is a consequence of rare many-body resonances, and is asymptotically larger than the typical eigenstate entanglement entropy. We verify these results numerically and discuss their connections to the many-body localisation transition.
List of changes
In the response to the referees comments we have:
- Included discussion of the connection to the locator expansion (Sec 3.1 p.8, Sec 3.2.2 p.11)
- Re-written discussion point "Connections to the many-body localisation finite-size crossover" to clarify the points discussed in our response to the referee's comments (Sec. 8 p.29).
- Corrected typos.
Published as SciPost Phys. 12, 103 (2022)
Reports on this Submission
Report #2 by Marco Rossi (Referee 1) on 2022-1-25 (Invited Report)
- Cite as: Marco Rossi, Report on arXiv:scipost_202106_00009v2, delivered 2022-01-25, doi: 10.21468/SciPost.Report.4232
Report
The paper concerns a detailed study of the interaction of a two level system with a bath.
The discussion is very general: various coupling regimes and different types of baths are studied, as the first referee remarks.
In particular the main novelty is the discussion of the weak and intermediate coupling regimes,
with the development of an ETH-like ansatz.
The paper is quite technical, but I appreciate that the results are proved and discussed
with a remarkable accuracy. Non trivial checks of the statements are provided by use of numerical
techniques and are illustrated in several useful pictures.
Therefore, in my opinion the paper deserves publication in the present form.
I just noticed some misprints:
1) at the beginning of page 6 should the open boundary condition involve \sigma ^x (and not
\sigma ^z)?
2) five lines after formula (34): relates -->related
3) five lines before formula (53): The the --->The