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arXiv · 2010.09728

Fractional Chiral Hinge Insulator

Anna Hackenbroich·Ana Hudomal·Norbert Schuch·B. Andrei Bernevig·Nicolas Regnault
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Abstract

We propose and study a wave function describing an interacting three-dimensional fractional chiral hinge insulator (FCHI) constructed by Gutzwiller projection of two non-interacting 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. By changing the boundary conditions for the underlying fermions, we investigate the topological degeneracy of the FCHI. Within the range of the numerically accessible system sizes, we observe a non-trivial topological degeneracy. A more numerically pristine characterization of the bulk topology is provided 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 a two-dimensional topological order with a TEE per surface compatible with half that of a Laughlin $1/2$ state, a value that cannot be obtained from topological quantum field theory.

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Anna Hackenbroich, Ana Hudomal, Norbert Schuch, B. Andrei Bernevig, Nicolas Regnault. 2020-10-19. Fractional Chiral Hinge Insulator. https://doi.org/10.1103/physrevb.103.l161110

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