Methods for Simulating Open Quantum Systems on Two-Dimensional Lattices with Tensor Networks

Tensor networks have been enormously successful at studying the quantum many body problem. By exploiting the structure of entanglement in a many-body quantum lattice system, a tensor network ansatz can accurately represent quantum state vectors with exponentially fewer parameters. While well known tensor network algorithms such as DMRG and TDVP are primarily used for the study of one-dimensional, closed systems, this presentation describes some state-of-the-art methods that can be applied to two-dimensional quantum systems evolving according to the Lindblad equation. Some new developments enabling the study of models with long-range interactions are also presented.