Experimentally Accessible Witnesses of Many-Body Localization

Round 1

Reviewer 1 Report

The authors investigated theoretically the many-body localization (MBL), with an aim of finding more feasible measurements of the relevant physics in the experiments to distinguish MBL. Referring to many-body physics, there usually exist huge gaps between theories and experiments, including many-body localization on which this paper is focused. In this work, the authors tried to reduce these gaps by proposing a list of quantities that are more accessible to the current experimental techniques.

It is actually a delight to read this paper. The manuscript is organized and written well; the ideas are presented in a clear way; the results seem solid with mathematic deductions and numerical simulations with tensor network. The only thing that worries me a litter is “if this propose can really be implemented in experiments and effectively distinguish MBL”. I believe it would be important and exciting if in the future we can see some more results by continuing the experimental efforts that was mentioned in the paper. In the current manuscript, I suggest the authors to add some more comments about the risks of implementing their proposal in experiments.

In summary, I recommend to accept this paper after minor revisions.

Author Response

We thank the referee for the positive report and the stimulating comments. To address the suggestion, we have added another subsection (5.4 Present and future experimental realizations), where we discuss the practical obstacles. These are mostly the repetition rate and the initial state preparation.

We hope to satisfactorily address the reviewer's suggestion with the following addition to the manuscript:

For an optical lattice architecture, the limitations of implementing the given measures are governed by the achievable repetition rate of the experiment and the quality of the initial state preparation. First of all, several repetitions are needed to get the expectation value of the measurements. Due to the disorder present in the system, it is furthermore necessary to repeat the first step with changing disorder to obtain a disorder averaged quantity. Lastly, since dynamics are in the focus of our measures, the described procedure needs to be carried out for any point in time. For linear quantities, such as Measure 1, Measure 3 or the imbalance, which is a measure of particle localization as well [21], the quantum average does in principle commute with the disorder average allowing for simultaneous averaging with fewer realizations. This is however not the case for non-linear quantities such as Measure 2. Here, the full procedure described above needs to be carried out. The repetition rates of optical lattices are on the order of seconds and leading experimentalists assured us that taking reliable data for all our measures is indeed feasible [44].

Reviewer 2 Report

see attached file

Comments for author File: Comments.pdf

Author Response

We thank the referee for their careful review of our manuscript. All typos were fixed. The 'provably' was indeed not a typo . To avoid confusion, we restructured the sentence and added the reference in which the proof is given. The new sentence now reads:

In the Anderson insulator in one-dimension, it is possible to prove that there exists a zero-velocity Lieb-Robinson-bound, where the correlator on the left hand side of Eq. (4) is bounded by a time independent factor e−μd( A,B) [44].