Topological Order at Non-zero Temperature

Details Topological Order at Non-zero Temperature Topological Order at Non-zero Temperature

2011-06-29

arxiv.org/abs/1106.6026v2

Phys. Rev. Lett. 107, 210501 (2011)

Physics

Quantum Physics

4 pages, 1 figure; added appendix describing toy example and also showing triviality of three dimensional toric code at T>0

Scientific paper

We propose a definition for topological order at nonzero temperature in analogy to the usual zero temperature definition that a state is topologically ordered, or "nontrivial", if it cannot be transformed into a product state (or a state close to a product state) using a local (or approximately local) quantum circuit. We prove that any two dimensional Hamiltonian which is a sum of commuting local terms is not topologically ordered at $T>0$. We show that such trivial states cannot be used to store quantum information using certain stringlike operators. This definition is not too restrictive, however, as the four dimensional toric code does have a nontrivial phase at nonzero temperature.

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