Quantum Matter Seminaar

Is every finite-time unitary dynamics determined by its total-time unitary operator? Clearly the answer is no because there can be small deformations of the dynamics at intermediate times. It has been appreciated that even if one ignores all those small deformations, the dynamics is still not specified by its total-time unitary operator; there are topological obstructions, which are well understood if unitary dynamics maps free fermions to free fermions. In this talk, we will discuss recent results in the "interacting" case on lattices of qudits (quantum spin systems). We will encounter an operator algebra on a 2d plane, in which one can construct a commuting Hamiltonian that realizes a chiral anyon theory.