Relaxation Exponents of OTOCs and Overlap with Local Hamiltonians

Round 1

Reviewer 1 Report

In the paper, the authors have studied certain relaxation property of otoc in quantum many body systems for local observables.
Their main finding is that the otoc relax in a way that depends on the commutator of the observable of interest and the local Hamiltonian (as well as exponent of it).  
The work is based on the method introduced in Ref.[39], in particular, making use of Lieb-robson bound and the assumption  of maximum scrambling, and the otoc at finite time is related to the infinite time otoc for finite volume.
An approximated formula for the infinite time averaged otoc is derived, showing that the system-size scaling behavior of the otoc depends on the lowest order of local hamiltonian that has a nonzero overlap with the observable.
Furthermore, the analytical results are also checked in a mixed field Ising model, and the numerical results agree quite well with the analytical prediction.

The main results are interesting. Indeed, generic analytical analysis of otoc has been found a hard topic and the achievements of this work is encouraging. Besides, the paper is well written. I recommend its publication in Entropy.

Comments for author File: Comments.pdf

Reviewer 2 Report

This paper provides an interesting extension of our understanding of out-of-time-order correlelators (OTOCs) by connecting algebraic decay exponents to the overlap of the observable in question with a power of the hamiltonian. The analysis is clear and backed-up with numerical computations. Publication is therefore recommended.