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A constructive theory of the numerically accessible many-body localized to thermal crossover
by Philip J D Crowley, Anushya Chandran
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Submission summary
| Authors (as registered SciPost users): | Philip Crowley |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202107_00043v1 (pdf) |
| Date submitted: | 2021-07-21 23:04 |
| Submitted by: | Crowley, Philip |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
The many-body localised (MBL) to thermal crossover observed in exact diagonalisation studies remains poorly understood as the accessible system sizes are too small to be in an asymptotic scaling regime. We develop a model of the crossover in short 1D chains in which the MBL phase is destabilised by the formation of many-body resonances. The model reproduces several properties of the numerically observed crossover, including an apparent correlation length exponent $\nu=1$, exponential growth of the Thouless time with disorder strength, linear drift of the critical disorder strength with system size, scale-free resonances, apparent $1/\omega$ dependence of disorder-averaged spectral functions, and sub-thermal entanglement entropy of small subsystems. In the crossover, resonances induced by a local perturbation are rare at numerically accessible system sizes $L$ which are smaller than a \emph{resonance length} $\lambda$. For $L \gg \sqrt{\lambda}$ (in lattice units), resonances typically overlap, and this model does not describe the asymptotic transition. The model further reproduces controversial numerical observations which Refs. [Suntajs et al 2019, Sels & Polkovnikov 2020] claimed to be inconsistent with MBL. We thus argue that the numerics to date is consistent with a MBL phase in the thermodynamic limit.
Current status:
Reports on this Submission
Strengths
- This is an extremely important contribution to the literature on finite-size effects in many-body localization.
- The paper is clearly written and the study is highly innovative.
Weaknesses
- I am not aware of any major weaknesses, I think the paper should be published as is.
Report
I think this is a very important paper and should be published as is.
Report #1 by Anonymous (Referee 2) on 2022-1-19 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202107_00043v1, delivered 2022-01-19, doi: 10.21468/SciPost.Report.4204
Report
In this work, the authors introduce a model for the description of the finite-size crossover properties in the vicinity of the putative MBL transition in one spatial dimension. Recent works in the field of MBL, in particular concerning exact diagonalization numerics for small system sizes, have raised serious questions on the MBL transition or even on the fundamental aspect of the very existence of the MBL phase. The key open problem at this point has been so far to understand the finite-size properties of strongly disordered systems when getting closer towards the (finite-size) MBL transition. In this context, the present work represents an important contribution to the field, especially because it is of analytical nature, and is very timely.
The manuscript is very well written and presents a variety of results, which all appear sound. Importantly, the results cover a very broad range of parameter regimes as well as physical observables. Further, the authors show that their analytical predictions match many of the numerical finite-size observations in the vicinity of the MBL transition, which is remarkable in my opinion. Consequently, this extensive manuscript certainly deserves publishing in SciPost. I just have a few minor comments, which might help to further improve the manuscript
1. To my taste the results of Refs. [1,2] are sometimes referred to in a bit subjective way, which doesn't always appear appropriate. For instance, on page 2 it is written that both Refs. [1,2] "claim that the numerical data precludes the possibility of an MBL phase altogether". I don't think that both papers actually claim that, the claims are partly weaker. Maybe it would be possible to weaken such statements slightly. By the way, both are now also published in journals.
2. When I understand correctly (see for instance Eq. (43)), the local perturbation studied in this manuscript is always in a weak coupling regime. Is that correct? In any case it would be good to clarify that prominently.
3. Section 2.3 on the thermal phase is rather brief. Although (as the authors say) the RM is not applicable, in the next sentence they say that RM still holds. This sounds a bit confusing and it would be good to clarify this. Further, the authors mention "almost-l-bits" without any reference. I feel that it is not clear what kind of l-bits these should be.
As soon as these minor aspects are taken into account, I would certainly recommend publication in SciPost.