Realizing the symmetry-protected Haldane phase in Fermi–Hubbard ladders

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 chain1,2. 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 parameter3,4. 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 entanglement5–7. 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.

Floquet's Refrigerator: Conformal Cooling in Driven Quantum Critical Systems

“…Here λ L is the Lyapunov exponent that characterizes the exponential growth of ||Π n || in (6), and will play the role of cooling rate in CFC. From (7), one can find energy density peaks located at x * which are determined by…”

“…Ultracold quantum gases, which can reach the nanokelvin regime, provide a new and controlled platform to investigate physics in a different realm. They have already been shown to exhibit novel phenomena, such as Bose-Einstein condensation, Mott-superfluid transition and are turning to the realization of exotic topological phases [2][3][4][5][6][7][8][9].…”

Interacting second-order topological insulators in one-dimensional fermions with correlated hopping

“…At the same time, an effective lattice dimerization can be realized by means of either a super-optical lattice [70,116] or optical tweezers arrays [117]. Finally, quantum gas microscopes have made possible to perform precise measurements of topological string correlation functions [69,118,119] to detect the symmetry protected topological phase. It appears thus natural to state that an efficient and accurate quantum simulation of our results can be realized and the interacting second-order topological insulator investigated.…”

“…Nevertheless, low dimensional higher-order topological crystalline phases remain an unexplored playground. Crucially, atomic quantum simulators have allowed to shed further light on this challenging topic by experimentally realize interacting topological matter [67][68][69][70]. Nevertheless, the experimental implementation of both single-particle and interacting higher order topological phases remain an unexplored playground.…”

Precise many-body simulations of antiferromagnetic phases using broken-symmetry perturbative expansions

“…Therefore, despite its apparent simplicity, the Hubbard model on the cubic lattice is an ideal platform to explore the potential of new algorithms before engaging in the study of more realistic systems. The model was realized in cold-atomic experiments on optical lattices where antiferromagnetism is under active investigation [17][18][19][20][21][22][23][24][25].…”