On the stability of the infinite Projected Entangled Pair Operator ansatz for driven-dissipative 2D lattices

Dainius Kilda; Alberto Biella; Marco Schiró; Rosario Fazio; Jonathan Keeling

doi:10.21468/SciPostPhysCore.4.1.005

On the stability of the infinite Projected Entangled Pair Operator ansatz for driven-dissipative 2D lattices

Dainius Kilda, Alberto Biella, Marco Schiró, Rosario Fazio, Jonathan Keeling

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Abstract

We present calculations of the time-evolution of the driven-dissipative 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 tensor-network ansatz. We discuss how more reliable results could be obtained.

Original language	English
Article number	005
Number of pages	19
Journal	SciPost Physics Core
Volume	Core 4
DOIs	https://doi.org/10.21468/SciPostPhysCore.4.1.005
Publication status	Published - 24 Feb 2021

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Kilda-2021-On-the-stability-SciPostPhysCore-4-1-005-CCBY
Copyright 2021 D. Kilda et al. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation.
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https://scipost.org/preprints/scipost_202012_00006v2/

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title = "On the stability of the infinite Projected Entangled Pair Operator ansatz for driven-dissipative 2D lattices",

abstract = "We present calculations of the time-evolution of the driven-dissipative XYZ model using the infinite Projected Entangled Pair Operator (iPEPO) method, introduced by [A. Kshetrimayum, H. Weimer and R. Or{\'u}s, 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 tensor-network ansatz. We discuss how more reliable results could be obtained.",

author = "Dainius Kilda and Alberto Biella and Marco Schir{\'o} and Rosario Fazio and Jonathan Keeling",

note = "Funding: DK acknowledges support from the EPSRC Condensed Matter Centre for Doctoral Training (EP/L015110/1); this research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. AB acknowledges funding by LabEx PALM (ANR-10-LABX-0039-PALM).",

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doi = "10.21468/SciPostPhysCore.4.1.005",

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T1 - On the stability of the infinite Projected Entangled Pair Operator ansatz for driven-dissipative 2D lattices

AU - Kilda, Dainius

AU - Biella, Alberto

AU - Schiró, Marco

AU - Fazio, Rosario

AU - Keeling, Jonathan

N1 - Funding: DK acknowledges support from the EPSRC Condensed Matter Centre for Doctoral Training (EP/L015110/1); this research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. AB acknowledges funding by LabEx PALM (ANR-10-LABX-0039-PALM).

PY - 2021/2/24

Y1 - 2021/2/24

N2 - We present calculations of the time-evolution of the driven-dissipative 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 tensor-network ansatz. We discuss how more reliable results could be obtained.

AB - We present calculations of the time-evolution of the driven-dissipative 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 tensor-network ansatz. We discuss how more reliable results could be obtained.

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DO - 10.21468/SciPostPhysCore.4.1.005

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VL - Core 4

JO - SciPost Physics Core

JF - SciPost Physics Core

M1 - 005

ER -

On the stability of the infinite Projected Entangled Pair Operator ansatz for driven-dissipative 2D lattices

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