Stable iPEPO Tensor-Network Algorithm for Dynamics of Two-Dimensional Open Quantum Lattice Models

Abstract

Being able to accurately describe the dynamics steady states of driven and/or dissipative but quantum correlated lattice models is of fundamental importance in many areas of science: from quantum information to biology. An efficient numerical simulation of large open systems in two spatial dimensions is a challenge. In this work, we develop a tensor network method, based on an infinite projected entangled pair operator ansatz, applicable directly in the thermodynamic limit. We incorporate techniques of finding optimal truncations of enlarged network bonds by optimizing an objective function appropriate for open systems. Comparisons with numerically exact calculations, both for the dynamics and the steady state, demonstrate the power of the method. In particular, we consider dissipative transverse quantum Ising, driven-dissipative hard-core boson, and dissipative anisotropic XY models in non-mean-field limits, proving able to capture substantial entanglement in the presence of dissipation. Our method enables us to study regimes that are accessible to current experiments but lie well beyond the applicability of existing techniques.