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Topologically ordered quantum spin systems have become an area of greatinterest, as they may provide a fault-tolerant means of quantum computation.One of the simplest examples of such a spin system is Kitaev's toric code.Naaijkens made mathematically rigorous the treatment of toric code on aninfinite planar lattice (the thermodynamic limit), using an operator algebraicapproach via algebraic quantum field theory. We adapt his methods to study thecase of toric code with gapped boundary. In particular, we recover thecondensation results described in Kitaev and Kong and show that the boundarytheory is a module tensor category over the bulk, as expected.

An algebraic quantum field theoretic approach to toric code with gapped boundary