From few to many


Fendley, P. (2010). From few to many. Perimeter Institute. https://pirsa.org/10050074


Fendley, Paul. From few to many. Perimeter Institute, May. 27, 2010, https://pirsa.org/10050074


          @misc{ pirsa_PIRSA:10050074,
            doi = {10.48660/10050074},
            url = {https://pirsa.org/10050074},
            author = {Fendley, Paul},
            keywords = {},
            language = {en},
            title = {From few to many},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {may},
            note = {PIRSA:10050074 see, \url{https://pirsa.org}}

Paul Fendley University of Oxford


I discuss a class of systems with a very special property: exact results for physical quantities can be found in the many-body limit in terms of the original (bare) parameters in the Hamiltonian. A classic result of this type is Onsager and Yang's formula for the magnetization in the Ising model. I show how analogous results occur in a fermion chain with strong interactions, closely related to the XXZ spin chain. This is done by exploiting a supersymmetry, and noting that certain quantites are independent of finite-size effects. I also discuss how these ideas are related to an interacting generalization of the Kitaev honeycomb model.