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Partial thermalisation of a two-state system coupled to a finite quantum bath

by Philip J. D. Crowley, Anushya Chandran

Submission summary

As Contributors: Philip Crowley
Preprint link: scipost_202106_00009v2
Date submitted: 2022-01-04 23:13
Submitted by: Crowley, Philip
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
  • Statistical and Soft Matter Physics
Approach: Theoretical


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.

Current status:
Editor-in-charge assigned

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.

Submission & Refereeing History

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Resubmission scipost_202106_00009v2 on 4 January 2022

Reports on this Submission

Anonymous Report 1 on 2022-1-6 (Invited Report)


The authors have improved the text and have followed all the suggestions given in the previous report. Therefore I think the paper can be published as it is.

  • validity: top
  • significance: high
  • originality: high
  • clarity: top
  • formatting: perfect
  • grammar: perfect

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