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On the stability of the infinite Projected Entangled Pair Operator ansatz for drivendissipative 2D lattices
by Dainius Kilda, Alberto Biella, Marco Schiro, Rosario Fazio, Jonathan Keeling
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Authors (as registered SciPost users):  Alberto Biella · Dainius Kilda · Marco Schirò 
Submission information  

Preprint Link:  scipost_202012_00006v1 (pdf) 
Code repository:  https://github.com/TheiPEPOProject/iPEPO 
Date submitted:  20201210 04:05 
Submitted by:  Kilda, Dainius 
Submitted to:  SciPost Physics Core 
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Academic field:  Physics 
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Approaches:  Theoretical, Computational 
Abstract
We present calculations of the timeevolution of the drivendissipative XYZ model using the infinite Projected Entangled Pair Operator (iPEPO) method, introduced by [A. Kshetrimayum, H. Weimer and R. Orús, Nat. Commun. 8, 1291 (2017)]. We explore the conditions under which this approach reaches a steady state. In particular, we study the conditions where apparently converged calculations may become unstable with increasing bond dimension of the tensornetwork ansatz. We discuss how more reliable results could be obtained.
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Anonymous Report 1 on 2021121 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202012_00006v1, delivered 20210121, doi: 10.21468/SciPost.Report.2446
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The manuscript ‘On the stability of the infinite Projected Entangled Pair Operator ansatz for drivendissipative 2D lattices’ by D. Kilda et al reproduces the earlier work of Kshetrimayum et al (Nat. Comm. 8, 1291 (2017)) and discusses the stability of the iPEPO algorithm at certain parameter regimes by looking at the dissipative XYZ model. They look at this model for different bond dimensions of the iPEPO and different initial states.
The study of open quantum system in 2D is a very challenging and important problem in physics and such works suggest that much remains to be done towards the numerical investigation of dissipative systems specially in the critical regimes. The paper is short but clear. While the findings of the paper are not surprising, I recommend its publication in SciPost Physics. However, I have some comments for which I would like to seek clarification from the authors.
1) Looking at Figure 1, the red regions correspond to the parameter regime where the iPEPO does not reach a steady state. They also correspond to the critical regimes which are difficult for Tensor networks in general even in closed systems. Similar result has been found in the original work of Nat. Comm. 8, 1291 (2017) where the authors compute the expectation value of the vectorized Liouvillian operator. Can the authors comment more elaborately on this?
2) In Fig. 1 again, the authors present results obtained using different Trotter steps. Can the authors explain why the results are so different for these particular regions? The trotter error coming from large step is of the order of \delta t^2 and this can be minimized by taking higher order trotterization. I recommend the authors to implement this and see if taking larger trotter steps help the calculation and if so, why.
3) In Fig. 2, the singular values for different parameter regimes are shown. However, it is not clear to me why the authors have shown only one singular value for each parameter. Is this the largest singular value? What happened to the rest of the singular values?
4) In Fig. 6, the authors take different bond dimensions and comment that some of the simulations could get unstable with increasing bond dimension. For simulations with D=10, 12, 14, 15, what is the bond dimension of the environment used here? Are these results correctly converged with the bond dimension of the environment?
In general, I feel that the authors present the result but does not offer much explanation or interpretation of the results. For example, why do different trotter step give different results, how their figure of merit is related to the results obtained by Kshetrimayum et al, how will the full update provide better stability, etc. I suggest the authors to take care of these things before publishing the manuscript.