Realization of the Symmetry-Protected Haldane phase in Fermi-Hubbard Ladder Systems

Sarah Hirthe, Pimonpan Sompet, Dominik Bourgund +9 more

J. P. Mendonça, S. Biswas, Marlena Dziurawiec +6 more

Pimonpan Sompet, Sarah Hirthe, Dominik Bourgund +10 more

Abstract Topology in quantum many-body systems has profoundly changed our understanding of quantum phases of matter. The model that has played an instrumental role in elucidating these effects is the antiferromagnetic spin-1 Haldane chain 1,2 . Its ground state is a disordered state, with symmetry-protected fourfold-degenerate edge states due to fractional spin excitations. In the bulk, it is characterized by vanishing two-point spin correlations, gapped excitations and a characteristic non-local order parameter 3,4 . More recently it has been understood that the Haldane chain forms a specific example of a more general classification scheme of symmetry-protected topological phases of matter, which is based on ideas connected to quantum information and entanglement 5–7 . Here, we realize a finite-temperature version of 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 enables us to investigate the robustness of the phase to charge (density) fluctuations far from the regime of the Heisenberg model, using a novel correlator.

Sanjay Moudgalya, Frank Pollmann

Anfuso and Rosch [Phys. Rev. B 75, 144420 (2007)] showed that the ``topological'' Haldane phase in a fermionic spin-$1/2$ ladder can be continuously deformed into a ``trivial'' phase without explicitly breaking symmetries when local charge fluctuations are taken into account. Within the framework of symmetry-protected topological phases, we revisit the model and demonstrate how the Haldane phase can be adiabatically connected to a trivial phase due to charge fluctuations. Furthermore, we show that the Haldane phase remains stable as long as the system is symmetric under particular reflection symmetries.

H. L. Nourse, Ian P. McCulloch, C. Janani +1 more

We demonstrate the existence of an insulating phase in the three-legged Hubbard ladder at two-thirds filling. In this phase chargons are bound because the physics within a unit cell favors the formation of triplets. The resultant moments lead to a ground state in the Haldane phase, a symmetry protected topological state of matter. In this purely fermionic model, reflection is protecting but time-reversal and dihedral symmetries are not, in contrast to spin models.

Hong Wei Yang, Hayate Nakano, Hosho Katsura