Three-dimensional topological phase on the diamond lattice

An interacting bosonic model of Kitaev type is proposed on the three-dimensional diamond lattice. Similarly to the two-dimensional Kitaev model on the honeycomb lattice which exhibits both Abelian and non-Abelian phases, the model has two (``weak'' and ``strong'' pairing) phases. In the weak pairing phase, the auxiliary Majorana hopping problem is in a topological superconducting phase characterized by a non-zero winding number introduced in A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, arXiv:0803.2786. The topological character of the weak pairing phase is protected by a discrete symmetry.Comment: 7 pages, 5 figure

Edge theory approach to topological entanglement entropy, mutual information and entanglement negativity in Chern-Simons theories

We develop an approach based on edge theories to calculate the entanglement entropy and related quantities in (2+1)-dimensional topologically ordered phases. Our approach is complementary to, e.g., the existing methods using replica trick and Witten's method of surgery, and applies to a generic spatial manifold of genus $g$, which can be bipartitioned in an arbitrary way. The effects of fusion and braiding of Wilson lines can be also straightforwardly studied within our framework. By considering a generic superposition of states with different Wilson line configurations, through an interference effect, we can detect, by the entanglement entropy, the topological data of Chern-Simons theories, e.g., the $R$-symbols, monodromy and topological spins of quasiparticles. Furthermore, by using our method, we calculate other entanglement measures such as the mutual information and the entanglement negativity. In particular, it is found that the entanglement negativity of two adjacent non-contractible regions on a torus provides a simple way to distinguish Abelian and non-Abelian topological orders.Comment: 30 pages, 8 figures; Reference and discussions on double torus are adde