Topological order in a 3D toric code at finite temperature

Details Topological order in a 3D toric code at finite temperature Topological order in a 3D toric code at finite temperature

2008-04-22

arxiv.org/abs/0804.3591v2

Phys. Rev. B 78, 155120 (2008)

Physics

Condensed Matter

Strongly Correlated Electrons

(28 pages, 9 figures)

Scientific paper

10.1103/PhysRevB.78.155120

We study topological order in a toric code in three spatial dimensions, or a 3+1D Z_2 gauge theory, at finite temperature. We compute exactly the topological entropy of the system, and show that it drops, for any infinitesimal temperature, to half its value at zero temperature. The remaining half of the entropy stays constant up to a critical temperature Tc, dropping to zero above Tc. These results show that topologically ordered phases exist at finite temperatures, and we give a simple interpretation of the order in terms of fluctuating strings and membranes, and how thermally induced point defects affect these extended structures. Finally, we discuss the nature of the topological order at finite temperature, and its quantum and classical aspects.

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