Sectorial Ground-State Nondegeneracy in Majorana Chains with Interaction and Orthogonal Symmetry

Abstract

Various quantum chains consisting of interacting Majorana fermions with flavors are constructed. These systems are invariant with respect to the rotations and reflections in the flavor space. The entire space of states splits into sectors characterized by a specific set of fermionic parities related to different flavors. All systems under consideration satisfy the Lieb-Mattis condition. As a result, the lowest-energy states within individual sectors are nondegenerate. The sectorial ground states are combined into antisymmetric (in flavor numbers) multiplets.