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.