Path Integrals Over Matrix Product States: Applications and Extensions

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The realisation that the ground states of short-range quantum spin systems can generically be represented by matrix product states is an important recent development in theoretical physics. With the aim of integrating the insights of matrix product states with the powerful tools of quantum field theory, Chris Hooley and some of his colleagues recently developed a path integral over one-dimensional versions of such states.The aim of this project is threefold: first, to explore the extension of this matrix-product-state path integral to higher-dimensional systems; second, to investigate the nature and physical meaning of instanton processes in such path integrals; and third, to develop further applications of the matrix-product-state path integral to open questions in the physics of frustrated magnetism.