Efficient Time Evolution of 2D Open-Quantum Lattice Models with Long-Range Interactions using Tensor Networks

Simulating many-body open quantum systems is an extremely challenging problem, with methods often restricted to either models with nearest-neighbor interactions or semi-classical approximations. In particular, modeling two-dimensional systems with realistic long-range interactions, in addition to dissipation, is of vital importance to the development of modern quantum computing and simulation platforms. We present a construction of the time-evolution operator, as a projected entangled pair operator (PEPO), that can be used to evolve a tensor network ansatz through time. Interactions beyond nearest-neighbor, including interactions between sites not collinear in the lattice, can be represented efficiently as a PEPO. Furthermore, we obtain approximations to realistic radial long-range interactions decaying with a power-law, that give accurate results with small operator bond dimension. Finally, we consider a physical example of a Rydberg atom Hamiltonian with long-range dipolar interactions, and show evidence of a dipole-dipole blockading effect in presence of dissipation. This work demonstrates the applicability of tensor networks to two-dimensional systems widely studied in experiments, but previously inaccessible to non-semi-classical methods.