Visualizing a Bosonic Symmetry Protected Topological Phase in an Interacting Fermion Model

TL;DR

This paper uses large-scale quantum Monte Carlo simulations to demonstrate that an interacting fermion lattice model can host an emergent bosonic symmetry protected topological phase characterized by gapped fermionic edges and gapless bosonic edge modes.

Contribution

First direct numerical evidence of an emergent bosonic SPT phase in an interacting fermionic lattice model using quantum Monte Carlo methods.

Findings

Fermion edge modes are gapped by interactions.

Bosonic edge modes remain gapless at the boundary.

System transitions to a trivial phase after a bulk quantum phase transition.

Abstract

Symmetry protected topological (SPT) phases in free fermion and interacting bosonic systems have been classified, but the physical phenomena of interacting fermionic SPT phases have not been fully explored. Here, employing large-scale quantum Monte Carlo simulation, we investigate the edge physics of a bilayer Kane-Mele-Hubbard model with zigzag ribbon geometry. Our unbiased numerical results show that the fermion edge modes are gapped out by interaction, while the bosonic edge modes remain gapless at the $(1+1)d$ boundary, before the bulk quantum phase transition to a topologically trivial phase. Therefore, finite fermion gaps both in the bulk and on the edge, together with the robust gapless bosonic edge modes, prove that our system becomes an emergent bosonic SPT phase at low energy, which is, for the first time, directly observed in an interacting fermion lattice model.