IAS Joint SNS/SOM High Energy Theory Seminar

Abstract: It is believed that topologically ordered gapped local Hamiltonians in 2+1d consisting of commuting terms may not realize a chiral anyon theory. There is even a formula that expresses the chiral central charge of the edge theory as an integral of commutators of the bulk Hamiltonian terms. Here, we follow an orthodox approach to quantum many-body physics to point out a strong but hidden role of tensor product algebras in this belief. We will give a locally generated, locally finite dimensional operator algebra on 2d and a local commuting Hamiltonian in that algebra, realizing the three-fermion anyon theory, which contradicts the belief. Furthermore, I will explain that the boundary of this three-fermion theory can be gapped out (but is not a boson condensate), again by some choice of a local operator algebra.