Haldane insulator protected by reflection symmetry in the doped Hubbard model on the three-legged ladder

TL;DR

This paper reveals a Haldane insulator phase in a doped three-legged Hubbard ladder, protected by reflection symmetry, showcasing a fermionic symmetry-protected topological state at two-thirds filling.

Contribution

It demonstrates the existence of a reflection-symmetry protected Haldane phase in a fermionic Hubbard model, expanding understanding of topological states in strongly correlated systems.

Findings

Insulating phase at two-thirds filling in the three-legged Hubbard ladder.

Formation of triplet-bound chargons leading to a Haldane phase.

Reflection symmetry protects the topological state, unlike time reversal or dihedral symmetries.

Abstract

We demonstrate the existence of an insulating phase in the three-legged Hubbard ladder at two-thirds filling. In this phase chargons are bound because the physics within a unit cell favors the formation of triplets. The resultant moments lead to a ground state in the Haldane phase, a symmetry protected topological state of matter. In this purely fermionic model, reflection is protecting but time reversal and dihedral symmetries are not, in contrast to spin models.