Tensor networks for quantum matter, quantum fields, and holography

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Quantum Mechanics provides us with the basic rules of how microscopic objects behave at the atomic and subatomic scales. However, when we place many such quantum objects together, we are not capable of theoretically predicting how they will behave collectively. For instance, even though we know that the electrons in a class of high-temperature superconducting materials (called cuprates) obey the laws of Quantum Mechanics, and believe that we have an accurate microscopic model for how they interact with each other, we have not yet been able to derive the emergence of superconductivity from that microscopic model. Tensor networks are a new way of representing the collective state of quantum many-body systems, based on recent improvements in our understanding of quantum entanglement. ***This Discovery Grant will advance and further develop the tensor network formalism in three important directions. Firstly, for quantum matter on the lattice (e.g. a lattice model of quantum spins for antiferromagnetic materials). Tensor networks were originally developed for lattice models of quantum matter, which are simplified models believed to capture the essential features of a many-body system. Secondly, for quantum fields directly in the continuum. Tensor networks for continuous systems are currently under construction, and could revolutionize how we think about and compute with strongly interacting quantum fields. Thirdly, tensor networks will be investigated as a realization of the holographic principle, which relates a theory of quantum gravity with a quantum field theory.***Thus, through a bold, multi-disciplinary research program in theoretical physics, this Discovery Grant aims to further strengthening Canada's leading role and international visibility in the areas of condensed matter, quantum information, computational physics, and high energy physics. The Grant will also contribute significantly to the training of highly qualified personnel, which will be exposed to fore-front research by leading experts in one of the world's most prestigious institutes for theoretical physics. ***********