Hubbard model for spin-1 Haldane chains

TL;DR

This paper demonstrates that the Haldane phase for spin-1 chains can be realized within a Hubbard model at half filling, connecting topological insulators to the Haldane phase through numerical evidence.

Contribution

It introduces a Hubbard model that encodes spin-1 Haldane chains, providing a new approach to simulate topological spin states with fermionic systems.

Findings

Haldane phase can be realized in a Hubbard model at half filling.

Noninteracting limit describes a 1D topological insulator.

The model is conjectured to be adiabatically connected to the Haldane phase.

Abstract

The Haldane phase for antiferromagnetic spin-1 chains is a celebrated topological state of matter, featuring gapped excitations and fractional spin-1/2 edge states. Here, we provide numerical evidence that this phase can be realized with a Hubbard model at half filling, where each $s=1$ spin is stored in a four-site fermionic structure. We find that the noninteracting limit of our proposed model describes a one-dimensional topological insulator, and we conjecture it to be adiabatically connected to the Haldane phase. Our work suggests a route to build spin-1 networks using Hubbard model quantum simulators.