Nagaoka ferromagnetism in doped Hubbard models in optical lattices

Abstract

The search for ferromagnetism in the Hubbard model has been a problem of outstanding interest since Nagaoka's original proposal in 1966. Recent advances in quantum simulation have today enabled the study of tunable doped Hubbard models in ultracold atomic systems. Employing large-scale density-matrix renormalization group calculations, we establish the existence of high-spin ground states of the Hubbard model on finite-sized triangular lattices, analyze the microscopic mechanisms behind their origin, and investigate the interplay between ferromagnetism and other competing orders, such as stripes. These results explain$\unicode{x2014}$and shed new light on$\unicode{x2014}$the intriguing observations of ferromagnetic correlations in recent optical-lattice experiments. Additionally, we examine a generalized variant of the Hubbard model, wherein any second electron on a single lattice site is weakly bound compared to the first one, and demonstrate how this modification can lead to enhanced ferromagnetism, at intermediate length scales, on the nonfrustrated square lattice as well.

6+5 pages, 4+2 figures

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Cited by in corpus (9)

• Observation of Nagaoka Polarons in a Fermi-Hubbard Quantum Simulator
• Directly imaging spin polarons in a kinetically frustrated Hubbard system
• Quantum Melting of Generalized Wigner Crystals in Transition Metal Dichalcogenide Moiré Systems
• Finite-Temperature Kinetic Ferromagnetism in the Square Lattice Hubbard Model
• Kinetic magnetism in the crossover between the square and triangular lattice Fermi-Hubbard models
• Instability of Nagaoka State and Quantum Phase Transition via Kinetic Frustration Control
• Optimal array geometries for kinetic magnetism and Nagaoka polarons
• Geometric Frustration Assisted Kinetic Ferromagnetism in Doped Mott Insulators
• Itinerant magnetism in Hubbard models with long-range interactions