DMRG Approach to Optimizing Two-Dimensional Tensor Networks

ITS Seminar with Katharine Hyatt (Flatiron Institute)

Tensor network algorithms have been remarkably successful solving a variety of problems in quantum many-body physics. However, algorithms to optimize two-dimensional tensor networks known as PEPS lack many of the aspects that make the seminal density matrix renormalization group (DMRG) algorithm so powerful for optimizing one-dimensional tensor networks known as matrix product states. We implement a framework for optimizing two-dimensional PEPS tensor networks which includes all of the steps that make DMRG so successful for optimizing one-dimension tensor networks. I will present results for several 2D spin models and discuss possible extensions and applications, including details about our approach, its advantages and drawbacks, and several open questions we are interested in addressing about the method and improvements to it.