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Using a description of the Levin-Wen model excitations in terms of Wilson lines, we compute the degeneracy of the energy levels for any input anyon theory and for any trivalent graph embedded on any (orientable) compact surface. This result allows one to obtain the finite-size and finite-temperature partition function and to show that there are no thermal phase transitions.
Our aim in this work is to study the nonequilibrium behavior of the topological quantum phase transition in the transverse Wen-plaquette model. We show that under the effect of a nonadiabatic driving the system exhibits a new topological phase and a
We study the spectrum of the long-range supersymmetric su$(m)$ $t$-$J$ model of Kuramoto and Yokoyama in the presence of an external magnetic field and a charge chemical potential. To this end, we first establish the precise equivalence of a large cl
It is known that every ribbon category with unimodality allows symmetrized $6j$-symbols with full tetrahedral symmetries while a spherical category does not in general. We give an explicit counterexample for this, namely the category $mathcal{E}$. We
The Olbertian partition function is reformulated in terms of continuous (Abelian) fields described by the Landau-Ginzburg action, respectively Hamiltonian. In order do make some progress, the Gaussian approximation to the partition function is transf
Do the SU(2) intertwiners parametrize the space of the EPRL solutions to the simplicity constraint? What is a complete form of the partition function written in terms of this parametrization? We prove that the EPRL map is injective for n-valent verte