Speaker
Description
Free fermions are a staple of theoretical physics, both in field theory and on the lattice. The traditional method for expressing bosonic lattice models in terms of them is via a non-linear ``Jordan-Wigner” transformation of the degrees of freedom. If the resulting action/Hamiltonian turns out to be a bilinear in fermions, you’re in luck. Recent years however have seen a more systematic approach, resulting in lattice Hamiltonians not expressible in terms of local fermionic bilinears but which nonetheless have a free-fermionic spectrum that can be computed exactly. I will describe such models with “free fermions in disguise” and what we know of their algebraic structure. I will also explain the open problem of finding a field theory describing them.