Tensor Networks for Chiral Topological Order

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This project aims at finding novel properties of topological phases of matter using the tools of entanglement and tensor networks. Specifically, the main goal is to develop an algorithm for numerically studying quantum many-body systems with 2d chiral topological order, which in turn correspond to the most relevant experimental realizations of materials with topological properties. The numerical method will be implemented using tensor network descriptions of quantum many- body states, such as finite and infinite Projected Entangled Pair States (PEPS). This proposed computational approach has never been implemented in the context of tensor network methods, and will constitute a very useful tool since it will allow calculations beyond the reach of current numerical methods. The resulting method will be a natural tool to study topological insulators and topological Mott insulators, where in many relevant cases a reliable numerical method is mainly missing. Moreover, our methods will also allow to study, as a by-product of the tensor network description, the many-body entanglement properties of these systems. This will be done using quantum information tools such as entanglement spectrum, topological entropy and topological geometric entanglement. The investigation of these quantities is expected to produce new insights into the physical mechanisms underlying the emergence of chiral topological quantum matter in 2d from microscopic degrees of freedom.