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Abstract: In this work the topological order at finite temperature in two-dimensionalcolor code is studied. The topological entropy is used to measure the behaviorof the topological order. Topological order in color code arises from thecolored string-net structures. By imposing the hard constrained limit the exactsolution of the entanglement entropy becomes possible. For finite size systems,by raising the temperature, one type of string-net structure is thermalized andthe associative topological entropy vanishes. In the thermodynamic limit theunderlying topological order is fragile even at very low temperatures. Takingfirst the thermodynamic limit and then the zero-temperature limit and viceversa does not commute, and their difference is related only to the topology ofregions. The contribution of the colors and symmetry of the model in thetopological entropy is also discussed. It is shown how the gauge symmetry ofthe color code underlies the topological entropy.



Author: Mehdi Kargarian

Source: https://arxiv.org/



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