Tensor networks and Legendre transforms


Swingle, B. (2017). Tensor networks and Legendre transforms. Perimeter Institute. https://pirsa.org/17040045


Swingle, Brian. Tensor networks and Legendre transforms. Perimeter Institute, Apr. 19, 2017, https://pirsa.org/17040045


          @misc{ pirsa_PIRSA:17040045,
            doi = {10.48660/17040045},
            url = {https://pirsa.org/17040045},
            author = {Swingle, Brian},
            keywords = {Condensed Matter, Quantum Fields and Strings, Quantum Gravity, Quantum Information},
            language = {en},
            title = {Tensor networks and Legendre transforms},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {apr},
            note = {PIRSA:17040045 see, \url{https://pirsa.org}}

Brian Swingle Brandeis University


Tensor networks have primarily, thought not exclusively, been used to the describe quantum states of lattice models where there is some inherent discreteness in the system. This raises issues when trying to describe quantum field theories using tensor networks, since the field theory is continuous (or at least the regulator should not play a central role). I'll present some work in progress studying tensor networks designed to directly compute correlation functions instead of the full state. Here the discreteness arises from our choice of where and how to probe the field theory. This approach is roughly analogous to studying a Legendre transform of the state. I'll discuss the properties of such networks and show how to construct them in some cases of interest, including non-interacting fermion field theories. Partly based on work with Volkher Scholz and Michael Walter.