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

TL;DR

This paper investigates the stability and reliability of the iPEPO tensor network method for simulating the driven-dissipative XYZ model in 2D lattices, focusing on steady-state convergence and potential instabilities.

Contribution

It analyzes the conditions affecting the stability of the iPEPO approach and proposes ways to obtain more reliable results for driven-dissipative quantum systems.

Findings

Identifies instability issues in iPEPO with increasing bond dimension.

Highlights the importance of convergence checks for steady-state calculations.

Suggests improved methods for reliable tensor network simulations.

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\'us, 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.