## SciPost Submission Page

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

### by Stefan Wolff, Ameneh Sheikhan, Corinna Kollath

### Submission summary

As Contributors: | Ameneh Sheikhan |

Preprint link: | scipost_202009_00014v1 |

Date submitted: | 2020-09-16 19:38 |

Submitted by: | Sheikhan, Ameneh |

Submitted to: | SciPost Physics Core |

Discipline: | Physics |

Subject area: | 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.

###### Current status:

### Submission & Refereeing History

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## Reports on this Submission

### Report 1 by Matteo Rizzi on 2020-9-21 Invited Report

### 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.