Finite-Temperature Kinetic Ferromagnetism in the Square Lattice Hubbard Model

Abstract

While the exact phase diagram of the Fermi-Hubbard model remains poorly understood despite decades of progress, nearly 60 years ago, Nagaoka proved that a single dopant in an otherwise half-filled Hubbard system can bring about ferromagnetism through kinetic means. The phenomenon was recently observed with ultracold atoms in triangular optical lattices. Here, we explore the kinetic ferromagnetism within the square lattice Hubbard model and its strong-coupling counterpart, the $t-J$ model, at finite temperatures in the thermodynamic limit via numerical linked-cluster expansions. We find evidence of ferromagnetic Nagaoka polarons at dopings up to $\sim 30\%$ away from half filling for a variety of interaction strengths and at temperatures as low as $0.2$ of the hopping energy. We map out the boundaries of this phase through analyzing various correlation functions.

11 pages, 10 figures

References in corpus (11)

• The Hubbard Model
• Numerical Linked-Cluster Approach to Quantum Lattice Models
• Coexistence of superconductivity with partially filled stripes in the Hubbard model
• A Short Introduction to Numerical Linked-Cluster Expansions
• Kinetic Magnetism in Triangular Moiré Materials
• Observation of Nagaoka Polarons in a Fermi-Hubbard Quantum Simulator
• Directly imaging spin polarons in a kinetically frustrated Hubbard system
• Finite-temperature superconducting correlations of the Hubbard model
• Polaronic mechanism of Nagaoka ferromagnetism in Hubbard models
• Nagaoka ferromagnetism in doped Hubbard models in optical lattices
• In situ controllable magnetic phases in doped twisted bilayer transition-metal dichalcogenides

Cited by in corpus (5)

• Instability of Nagaoka State and Quantum Phase Transition via Kinetic Frustration Control
• Functional renormalization group for extremely correlated electrons
• Finite temperature dopant-induced spin reorganization explored via tensor networks in the two-dimensional $t$-$J$ model
• Bad Metal Behavior and Lifshitz Transition of a Nagaoka Ferromagnet
• Shaping Magnetic Order by Local Frustration for Itinerant Fermions on a Graph