Long range toric code: finite temperature topological order in two dimensions

In traditional 2D topological order, anyons quasiparticles are deconfined: the energy required to separate two anyons arbitrarily far apart is finite.As a result, thermally excited anyons proliferate and destroy topological order at anyfinite temperature.

We introduce an extension of the toric code with long-range,power law interactions that maintains topological order at nonzero temperatures. Theinteractions generate a confining potential between anyons, stabilizing the topologicalphase against thermal fluctuations. For several forms of long-range couplings, weidentify a confining topological phase below a critical temperature, where the groundstate is topologically ordered but the excitations remain confined.