Partition function of the Kitaev quantum double model
Jean-Noël Fuchs (LPTMC, Paris)
In this talk, I will discuss our recent work on the Kitaev quantum double model [1]. This is an exactly-solvable lattice gauge theory built on a discrete group G and on a 2D graph. Its excitations are deconfined anyons. Its simplest instance is the famous toric code model built from the Z_2 group. Even more interesting physics occurs when G is non-Abelian. The energy spectrum of the model is trivial (the energy levels are equidistant) but their degeneracy is not when G is non-Abelian. This comes from the fact that non-Abelian anyons can have several fusion channels. In this work, I will show how we computed the corresponding fusion degeneracies using the machinery of tensor categories. This allowed us to obtain the partition function and many finite-temperature properties. In particular, we find that this type of topological order (à la Wen) is destroyed at any finite temperature in the thermodynamic limit. However, in a finite-size system, there is a finite temperature below which topological order is preserved.
[1] A. Ritz-Zwilling, B. Douçot, S. H. Simon, J. Vidal, and J.-N. Fuchs, arXiv:2509.10876, Phys. Rev. B 113, 165106 (2026).