Tensor network approaches to quantum many-body phenomena

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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 put 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. My research program is based on further developing the formalism of tensor networks for quantum many-body systems both in the discrete (lattice models, such as models of quantum spins for antiferromagnetic materials) and in the continuum (quantum field theories, used in particle physics). I will also apply these novel techniques to a range of open problems in several areas of science and technology where quantum many-body phenomena play a prominent role, foremost condensed matter and high energy physics, but also quantum chemistry, nanotechnology, quantum computation and string theory.