Laboratoire de Physique Théorique
Toulouse - UMR 5152

Tensor networks have already proven to be extremely useful tools in the studies of strongly correlated quantum systems. Being immune to the sign problem, they enable calculations beyond Quantum Monte Carlo and directly in the thermodynamic limit. The most established and understood tensor network method is density matrix renormalization group (DMRG), while all others, including projected entangled pair states (PEPS) seemed to remain far behind until recently, when an automatic differentiation framework was established. This toolbox, originally developed for the deep learning purposes, enables a simple calculation of exact derivatives in an optimization problem at hand and hence bridges the gap between DMRG and PEPS simulations. I will try to deliver a multi-level talk, starting with a comprehensive introduction of tensor network methods with focus on iPEPS before delving into details of derivative calculation for optimization purposes. On the example of Corner Transfer Matrix (CTM) I will explain the idea of algorithmic differentiation, present possible challenges and show ways to overcome them.