Fermionic projected entangled-pair states and topological phases

Abstract

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 ${\mathbb{Z}}_2$ 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.

Published version

References in corpus (4)

• Gauging quantum states: from global to local symmetries in many-body systems
• Fermionic Matrix Product States and One-Dimensional Topological Phases
• Symmetries and boundary theories for chiral Projected Entangled Pair States
• Grassmann tensor network states and its renormalization for strongly correlated fermionic and bosonic states