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Accueil du site > Séminaires > Séminaires 2007 > Classical and quantum topological order : the birth of a coherent picture

Mardi 22/05/2007 - 14H00

Classical and quantum topological order : the birth of a coherent picture

Claudio Castelnovo (Oxford - UK)

par Didier Poilblanc - 22 mai 2007

We calculate exactly the von Neumann and topological entropies of the toric code as a function of system size and temperature. We do so for systems with infinite energy scale separation between magnetic and electric excitations, so that the magnetic closed loop structure is fully preserved while the electric loop structure is tampered with by thermally excited electric charges. We find that the topological entropy drops to half its zero-temperature value for any infinitesimal temperature in the thermodynamic limit, and remains constant as the temperature is further increased. Such discontinuous behavior is replaced by a smooth decreasing function in finite-size systems. If the separation of energy scales in the system is large but finite, we argue that our results hold at small enough temperature and finite system size, and a second drop in the topological entropy occurs as the temperature is raised so as to disrupt the magnetic loop structure by allowing the appearance of free magnetic charges. We interpret our results as an indication that the underlying magnetic and electric closed loop structures contribute equally to the topological entropy (and therefore to the topological order) in the system. Since each loop structure \emphper se is a classical object, we interpret the quantum topological order in our system as arising from the ability of the two structures to be superimposed and appear simultaneously.