New Publication in Journal of Physics A: Mathematical and Theoretical


Our publication on Fermionic projected entangled-pair states and topological phases was published in Journal of Physics A: Mathematical and Theoretical.

We study fermionic matrix product operator algebras and identify the associated algebraic data. Using this algebraic data we construct fermionic tensor network states in two dimensions that have non-trivial symmetry-protected or intrinsic topological order. The tensor network states allow us to relate physical properties of the topological phases to the underlying algebraic data. We illustrate this by calculating defect properties and modular matrices of supercohomology phases. Our formalism also captures Majorana defects as we show explicitly for a class of symmetry-protected and intrinsic topological phases. The tensor networks states presented here are well-suited for numerical applications and hence open up new possibilities for studying interacting fermionic topological phases.


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Schematic representation of the two paths giving rise to the super pentagon equation. The upper path consists of three F-moves and is similar to the bosonic case. In the lower path there are two F-moves and one fermionic reordering of the fusion tensors, leading to a potential minus sign depending on their parity.