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arXiv:1312.6672 · Physical Review Letters

Classical Antiferromagnetism in Kinetically Frustrated Electronic Models

Cintia N. Sposetti, Barbara Bravo, A. E. Trumper, C. J. Gazza, L. O. Manuel

Published May 9, 2014• 37 citations
arXivHTMLPDF

Abstract

We study, by means of the density matrix renormalization group, the infinite U Hubbard model--with one hole doped away from half filling--in triangular and square lattices with frustrated hoppings, which invalidate Nagaoka's theorem. We find that these kinetically frustrated models have antiferromagnetic ground states with classical local magnetization in the thermodynamic limit. We identify the mechanism of this kinetic antiferromagnetism with the release of the kinetic energy frustration, as the hole moves in the established antiferromagnetic background. This release can occur in two different ways: by a nontrivial spin Berry phase acquired by the hole, or by the effective vanishing of the hopping amplitude along the frustrating loops.

DOI
10.1103/physrevlett.112.187204

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We study, by means of the density matrix renormalization group, the infinite U Hubbard model--with one hole doped away from half filling--in triangular and square lattices with frustrated hoppings, which invalidate Nagaoka's theorem. We find that these kinetically frustrated models have antiferromagnetic ground states with classical local magnetization in the thermodynamic limit. We identify the mechanism of this kinetic antiferromagnetism with the release of the kinetic energy frustration, as the hole moves in the established antiferromagnetic background. This release can occur in two different ways: by a nontrivial spin Berry phase acquired by the hole, or by the effective vanishing of the hopping amplitude along the frustrating loops.
We investigate, using the density-matrix renormalization group, the evolution of the Nagaoka state with ${t}^{\ensuremath{'}}$ hopping that frustrates the hole kinetic energy in the $U=\ensuremath{\infty}$ Hubbard model on the square and anisotropic triangular lattices. We find that the Nagaoka ferromagnet survives up to a rather small ${t}_{c}^{\ensuremath{'}}/t\ensuremath{\sim}0.2.$ At this critical value, there is a transition to an antiferromagnetic phase that depends on the lattice: a Q=(Q,0)\mathbf{Q}=(Q,0)Q=(Q,0) spiral order, which continuously evolves with ${t}^{\ensuremath{'}}$, for the triangular lattice and the usual $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$ N\'eel order for the square lattice. Remarkably, the local magnetization takes its classical value for all considered ${t}^{\ensuremath{'}}$ (${t}^{\ensuremath{'}}/t\ensuremath{\le}1$). Our results show that the recently found classical kinetic antiferromagnetism, a perfect counterpart of Nagaoka ferromagnetism, is a generic phenomenon in these kinetically frustrated electronic systems.
We investigate the Nagaoka-Thouless ferromagnetic instability in the strongly interacting t − t ′ Hubbard model by continuously breaking particle-hole symmetry on a tunable square-triangular lattice geometry. We use an analytic approach to show that the fully spin-polarized state becomes unstable to a metastable spin polaron when the kinetic frustration t ′ / t exceeds a critical, dimension-dependent value. Large-scale density matrix renormalization group simulations reveal a quantum phase transition from the Nagaoka ferromagnet to a spiral spin-density wave, which evolves continuously into the Haerter-Shastry antiferromagnet in the large-frustration limit. Remarkably, this transition remains robust at low but finite hole density, making it accessible in cold-atom and moiré Hubbard platforms under strong interactions. A variational analysis further captures the instability mechanism at finite hole density via frustration-induced magnon band deformation.
Abstract The fermionic Hubbard model, when combined with frustration, associated with the breaking of particle-hole symmetry, harbors a rich phase diagram. Theoretical findings associated with the nature of magnetism and metallicity across this phase diagram are now being actively investigated in triangular Hubbard cold atom and solid-state (moiré) based emulators. Building on the theoretical work of Haerter and Shastry, we explore the impact of kinetically frustrated magnetism, a phenomenon where antiferromagnetic order emerges without any underlying magnetic interactions, at finite hole density. We numerically study the infinite- U triangular Hubbard model using the density matrix renormalization group algorithm and estimate the stability of the kinetically induced 120 ∘ antiferromagnetic state to hole doping. Beyond the Haerter-Shastry regime, we find an intermediate phase with multimer (involving multiple correlated spins) stripes that eventually gives way to a paramagnet. We also find evidence of gapless charge excitations (metallicity) throughout the phase diagram for finite hole density. We discuss the implications at large, but finite, values of U / t , and investigate whether kinetic magnetism and superexchange collaborate or compete.
We study kinetic magnetism for the Fermi-Hubbard models in triangular type lattices, including a zigzag ladder, four- and six-legged triangular cylinders and a full two-dimensional triangular lattice. We focus on the regime of strong interactions, U≫tU\gg tU≫t and filling factors around one electron per site. For temperatures well above the hopping strength, the Curie-Weiss form of the magnetic susceptibility suggests effective antiferromagnetic correlations for systems that are hole doped with respect to ν=1ν=1ν=1, and ferromagnetic correlations for systems with electron dopings. We show that these correlations arise from magnetic polaron dressing of charge carrier propagating in a spin incoherent Mott insulator. Effective interactions corresponding to these correlations can strongly exceed the magnetic super-exchange energy. In the case of hole doping, antiferromagnetic polarons originate from kinetic frustration of individual holes in a triangular lattice. In the case of electron doping, Nagaoka type ferromagnetic correlations are induced by propagating doublons. These results provide a theoretical explanation of recent experimental results in moire TMDC materials. To understand many-body states arising from antiferromagentic polarons at low temperatures, we study hole doped systems in finite magnetic fields. At low dopings and intermediate magnetic fields we find a magnetic polaron phase, separated from the fully polarized state by a metamagnetic transition. With decreasing magnetic field the system shows a tendency to phase separate, with hole rich regions forming antiferromagnetic spinbags. We demonstrate that direct observations of magnetic polarons in triangular lattices can be achieved in experiments with ultracold atoms, which allow measurements of three point hole-spin-spin correlations.
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 $t\ensuremath{-}J$ model, at finite temperatures in the thermodynamic limit via numerical linked-cluster expansions. We find evidence of ferromagnetic Nagaoka polarons at dopings up to $\ensuremath{\sim}30%$ 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.
Understanding ferromagnetism mechanism in doped Mott insulators on frustrated lattices remains challenging at intermediate coupling and finite doping. Here, we study the itinerant ferromagnetism and propose its mechanism in doped Mott insulators on a geometrically frustrated triangular lattice. Using large-scale density matrix renormalization group (DMRG) and unrestricted Hartree–Fock mean-field methods, we reveal that itinerant ferromagnetism appears at intermediate coupling (10 ≲ U ≪ ∞) near 50% electron doping in the triangular-lattice Hubbard model. By analyzing all microscopic hopping processes, we find that doublon-singlon exchange alone drives the fully polarized ferromagnetism and uncovers the particle-hole asymmetry. We also establish the magnetic phase diagram and compare local spin correlations with recent experiments. Random phase approximation and DMRG calculations consistently confirm that the ferromagnetism persists when SU(2) symmetry is explicitly broken by magnetic anisotropy. These results clarify a microscopic route to itinerant ferromagnetism at intermediate coupling and finite doping in doped Mott insulators. Understanding the mechanism of ferromagnetism in strongly correlated systems is an ongoing theoretical challenge and the Hubbard model is typically adopted to investigate such systems. Here, the authors numerically investigate the doped triangular Fermi-Hubbard model and show ferromagnetism at intermediate coupling and finite doping, which results from the interplay of kinetic doublon-singlon exchange and lattice geometry.