Absence of topological degeneracy in the Hubbard model on honeycomb lattice

TL;DR

This paper demonstrates that the Hubbard model on a honeycomb lattice lacks topological degeneracy due to its unique sign structure, which remains unaffected by $Z_{2}$ gauge flux, contrasting with expectations for topologically ordered systems.

Contribution

It reveals that the ground state sign structure in the honeycomb Hubbard model prevents topological degeneracy, providing insight into the relationship between sign structure and topological order.

Findings

Ground state sign structure is insensitive to $Z_{2}$ gauge flux.

Absence of topological degeneracy in the honeycomb Hubbard model.

Variational states illustrate the link between sign structure and topological properties.

Abstract

It is shown that the unique sign structure of the ground state of the Hubbard model on honeycomb lattice, which is shown to be insensitive to the trapped $Z_{2}$ gauge flux when the system is defined on a torus, may cause the absence of topological degeneracy on this bipartite system. Examples of variational Mott insulating state on the honeycomb lattice are given to illustrate the close relation between the sign structure of the ground state and the (absence of) topological degeneracy.