We propose and study a wave function describing an interacting three-dimensional fractional chiral hinge insulator (FCHI) constructed by Gutzwiller projection of two noninteracting second-order topological insulators with chiral hinge modes at half filling. We use large-scale variational Monte Carlo computations to characterize the model states via the entanglement entropy and charge-spin fluctuations. We show that the FCHI possesses fractional chiral hinge modes characterized by a central charge $c=1$ and Luttinger parameter $K=1/2$, like the edge modes of a Laughlin $1/2$ state. The bulk and surface topology is characterized by the topological entanglement entropy (TEE) correction to the area law. While our computations indicate a vanishing bulk TEE, we show that the gapped surfaces host an unconventional two-dimensional topological phase. In a clear departure from the physics of a Laughlin $1/2$ state, we find a TEE per surface compatible with $(ln\sqrt{2})/2$, half that of a Laughlin $1/2$ state. This value cannot be obtained from topological quantum field theory for purely two-dimensional systems. For the sake of completeness, we also investigate the topological degeneracy.

• Received 26 October 2020
• Accepted 2 April 2021

DOI:https://doi.org/10.1103/PhysRevB.103.L161110