Tensor Network Algorithims for Simulating Many-Body Open Quantum Systems in Two Dimensions

Quantum many-body systems in the presence of drive and dissipation are some of the more difficult problems to solve numerically. Algorithms based on tensor networks have found great success in the context of closed quantum systems, and open systems in one-dimension, however their extension to two-dimensional open quantum systems has only recently come to fruition. In this presentation, a tensor network aglorithm based on the infinite projected entangled pair operator (iPEPO) ansatz detailed in Ref. [1] utilising the matrix-product operator (MPO) appoximation of the dynamical map, rather than Trotter gates, will be discussed. MPOs have the potential to represent long-range interactions and tend to be computationally less expensive. We demonstrate the accuracy of the results by comparing to exact solutions, and demonstrate that the algorithm remains stable when moving away from the exactly solveable regime. This tensor network algorithm can be used to obtain the steady states and transient dynamics of two-dimensional quantum lattice models evolving according to the Lindblad equation

[1]. C. Mc Keever and M. H. Szymańska, Phys. Rev. X 11, 021035 (2021)