Toric codes and quantum doubles from two-body Hamiltonians

Abstract

We present a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the low-energy limits of entirely two-body Hamiltonians. Our construction makes use of a new type of perturbation gadget based on error-detecting subsystem codes. The procedure is motivated by a PEPS description of the target models, and reproduces the target models' behavior using only couplings which are natural in terms of the original Hamiltonians. This allows our construction to exactly capture the symmetries of the target models.

10 pages of ideas plus 26 pages of calculations; 8 figures. v2, improved discussion of perturbation theory and relation to other topological subsystem codes; refs added. v3, v4, minor corrections and clarifications; published version