Two dimensional gauge invariant tensor networks

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The study of correlated quantum many-body systems in and out of equilibrium - despite being at the heart of our understanding of Nature - remains one of the big challenge of quantum physics. Analytical and numerical methods available are in many cases strongly limited and allow to describe only an approximated version of the physics of interests. In the lat decade, tensor network methods opened new possibilities and are now a standard tool to simulate one-dimensional correlated quantum dynamics. However, two-dimensional many-body quantum system dynamics are still out of reach of numerical simulations in most interesting settings. Providing novel numerical algorithms to solve this challenge, would shade light into different fields of physics as quantum technologies, quantum field theories, condensed matter and critical phenomena. Building on some recent developments I have introduced for one-dimensional systems -lattice gauge tensor networks, optimal control theory, and hierarchical tensor networks- together with high- performance computing, this project aims to take unprecedented steps towards: - the development of numerical simulations methods for two-dimensional lattice gauge theories; - the study of open problems that nowadays hinder the development of quantum technologies and our understanding of the properties of frustrated spin systems (quantum dimer models, valence bond states), topological models, and high-energy two dimensional models on a lattice describing aspects of quantum electrodynamics and chromodynamics. This project will pave the way to investigations in unchartered territory with impact on fundamental aspects of correlated many-body quantum physics. The results of this project will serve also as highly non trivial benchmarks for the first generation of quantum simulators, and - due to the extreme complexity of their implementation - for their verification.