Numerical evaluation of two-time correlation functions in open quantum systems with matrix product state methods: a comparison

Submission summary

 As Contributors: Ameneh Sheikhan Preprint link: scipost_202009_00014v1 Date accepted: 2020-10-30 Date submitted: 2020-09-16 19:38 Submitted by: Sheikhan, Ameneh Submitted to: SciPost Physics Core Academic field: Physics Specialties: Condensed Matter Physics - Computational Approach: Computational

Abstract

We compare the efficiency of different matrix product state (MPS) based methods for the calculation of two-time correlation functions in open quantum systems. The methods are the purification approach [1] and two approaches [2,3] based on the Monte-Carlo wave function (MCWF) sampling of stochastic quantum trajectories using MPS techniques. We consider a XXZ spin chain either exposed to dephasing noise or to a dissipative local spin flip. We find that the preference for one of the approaches in terms of numerical efficiency depends strongly on the specific form of dissipation.

Published as SciPost Phys. Core 3, 010 (2020)

Submission & Refereeing History

Resubmission scipost_202009_00014v1 on 16 September 2020
Submission 2004.01133v1 on 3 April 2020

Reports on this Submission

Anonymous Report 2 on 2020-9-30 (Invited Report)

• Cite as: Anonymous, Report on arXiv:scipost_202009_00014v1, delivered 2020-09-30, doi: 10.21468/SciPost.Report.2033

Report

Most of the remarks of the previous reports were taken into account and the remaining ones were answered with detailed and convincing arguments.

Only one tiny remark:
Please also remove the system size in the error in Fig. 2 and, while already working on this figure, also change the $O$ in the first line.

• validity: high
• significance: good
• originality: good
• clarity: high
• formatting: good
• grammar: good

Report 1 by Matteo Rizzi on 2020-9-21 (Invited Report)

• Cite as: Matteo Rizzi, Report on arXiv:scipost_202009_00014v1, delivered 2020-09-21, doi: 10.21468/SciPost.Report.2013

Report

I am glad to say that the Authors have satisfactorily addressed most of the issues raised in the two previous referee reports, and have provided sound arguments not to implement some of the suggested modifications.
Certainly, some questions might be seen as matter of taste ones and it is the full freedom of the Authors to chose how to present their own material: therefore I fully consider the manuscript to be publishable in its present form.
Meanwhile let me thank the Authors also for having clarified some little misunderstandings in my first reading -- given the public availability of reports and replies on SciPost, this would be of help for future readers with similar doubts, too.

Two incidental remarks:
i) The clarification about the wall clock/CPU time of the algorithm is very transparent and indeed of great help for the reader interested into implementing such algorithms and estimating the workflow for answering a research question;
ii) About the error estimates in Eqs. (46-48) (of which at point L in my previous report), I was simply curious to know why the same have been used only for the first case of dissipation and not the second one, and what would have been the outcome of such an analysis -- I probably messed it up in mixing two different questions, sorry.

• validity: high
• significance: good
• originality: good
• clarity: high
• formatting: good
• grammar: good