CMT Forum: Paul Fendley

Free fermions are ubiquitous in theoretical physics. Typically such models are found by expressing the Hamiltonian and/or action as a sum or integral over bilinears of local fermionic operators or fields, sometimes requiring a Jordan-Wigner transformation. I describe models that become free fermionic only after under a much subtler transformation that is both non-local and non-linear in the original interacting fermions. I also will explain how encoding Hamiltonians in a graph allows one to identify models solvable by this approach.