Realising the Symmetry-Protected Haldane Phase in Fermi-Hubbard Ladders

TL;DR

This paper demonstrates the realization of the symmetry-protected Haldane phase in Fermi-Hubbard ladders using ultracold atoms, revealing edge and bulk properties through advanced measurements and exploring phase robustness across interaction strengths.

Contribution

It introduces a method to realize and probe the topological Haldane phase in Fermi-Hubbard ladders with ultracold atoms, extending understanding of SPT phases.

Findings

Successful realization of the Haldane phase in Fermi-Hubbard ladders

Direct measurement of edge and bulk properties of the topological phase

Robustness of the phase against charge fluctuations across interaction strengths

Abstract

Topology in quantum many-body systems has profoundly changed our understanding of quantum phases of matter. The paradigmatic model that has played an instrumental role in elucidating these effects is the antiferromagnetic spin-1 Haldane chain. Its ground state is a disordered state, with symmetry-protected fourfold-degenerate edge states due to fractional spin excitations. In the bulk, it is characterised by vanishing two-point spin correlations, gapped excitations, and a characteristic non-local order parameter. More recently it was understood that the Haldane chain forms a specific example of a more general classification scheme of symmetry protected topological (SPT) phases of matter that is based on ideas connecting to quantum information and entanglement. Here, we realise such a topological Haldane phase with Fermi-Hubbard ladders in an ultracold-atom quantum simulator. We directly reveal both edge and bulk properties of the system through the use of single-site and particle-resolved measurements as well as non-local correlation functions. Continuously changing the Hubbard interaction strength of the system allows us to investigate the robustness of the phase to charge (density) fluctuations far from the regime of the Heisenberg model employing a novel correlator.