46 research outputs found
Finite temperature topological order in 2D topological color codes
In this work the topological order at finite temperature in two-dimensional
color code is studied. The topological entropy is used to measure the behavior
of the topological order. Topological order in color code arises from the
colored string-net structures. By imposing the hard constrained limit the exact
solution of the entanglement entropy becomes possible. For finite size systems,
by raising the temperature, one type of string-net structure is thermalized and
the associative topological entropy vanishes. In the thermodynamic limit the
underlying topological order is fragile even at very low temperatures. Taking
first the thermodynamic limit and then the zero-temperature limit and vice
versa does not commute, and their difference is related only to the topology of
regions. The contribution of the colors and symmetry of the model in the
topological entropy is also discussed. It is shown how the gauge symmetry of
the color code underlies the topological entropy.Comment: 20 pages, 5 figure