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arXiv:2402.14074

Itinerant magnetism and magnetic polarons in the triangular lattice Hubbard model

Ivan Morera, Eugene Demler

Published Feb 21, 2024• 0 citations
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Abstract

We use density matrix renormalization group to investigate the phase diagram of the Fermi Hubbard model on a triangular lattice with densities above half-filling, $1 \leq n < 2$. We discuss the important role of kinetic magnetism and magnetic polarons. For strong interactions and low doublon dopings, attractive interaction between polarons results in phase separation between the fully polarized state at finite doping and the commensurate spin-density wave state at half-filling. For intermediate interaction strength and small doping, competition between antiferromagnetic superexchange and kinetic magnetism gives rise to the incommensurate spin density wave (I-SDW) phase. Fully polarized ferromagnetic (FPF) phase for weak interactions is limited to dopings close to the van Hove singularity in the density of states. With increasing interactions the FPF phase expands to lower dopings. For strong interactions it reaches the low doping regime and is better understood as arising from proliferation of Nagaoka-type ferromagnetic polarons. Other phases that we find include a partially polarized phase, another type of I-SDW at high densities, and Müller-Hartmann ferromagnetism close to the band insulating regime.

DOI
10.48550/arxiv.2402.14074

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We use density matrix renormalization group to investigate the phase diagram of the Fermi Hubbard model on a triangular lattice with densities above half-filling, 1≤n<21 \leq n < 21≤n<2. We discuss the important role of kinetic magnetism and magnetic polarons. For strong interactions and low doublon dopings, attractive interaction between polarons results in phase separation between the fully polarized state at finite doping and the commensurate spin-density wave state at half-filling. For intermediate interaction strength and small doping, competition between antiferromagnetic superexchange and kinetic magnetism gives rise to the incommensurate spin density wave (I-SDW) phase. Fully polarized ferromagnetic (FPF) phase for weak interactions is limited to dopings close to the van Hove singularity in the density of states. With increasing interactions the FPF phase expands to lower dopings. For strong interactions it reaches the low doping regime and is better understood as arising from proliferation of Nagaoka-type ferromagnetic polarons. Other phases that we find include a partially polarized phase, another type of I-SDW at high densities, and Müller-Hartmann ferromagnetism close to the band insulating regime.
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.
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.
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.
We use unrestricted Hartree-Fock, density matrix renormalization group, and variational projected entangled-pair state calculations to investigate the ground-state phase diagram of the triangular-lattice Hubbard model at “half doping” relative to single occupancy, i.e., at fillings of ( 1 ± 1 2 ) electrons per site. The electron-doped case has a nested Fermi surface in the noninteracting limit, and hence a weak-coupling instability toward density-wave orders whose wave vectors are determined by Fermi-surface nesting conditions. We find that at moderate-to-strong interaction strengths, other spatially modulated orders arise, with wave vectors distinct from the nesting vectors. In particular, we identify a series of closely competing, itinerant long-wavelength magnetically ordered states, yielding to uniform ferromagnetic order at the largest interaction strengths. For half-hole doping and a similar range of interaction strengths, our data indicate that magnetic orders are most likely absent.
A wide variety of experimental platforms, ranging from semiconductor quantum-dot arrays to moiré materials, have recently emerged as powerful quantum simulators for studying the Hubbard model and its variants. Motivated by these developments, here, we investigate a generalization of the Hubbard model which includes the effects of long-range Coulomb interactions. Working on finite-sized two-dimensional square and triangular lattices, we use exact diagonalization and density-matrix renormalization group calculations to probe the magnetic structure of the ground state in the strong-coupling regime, where UUU (the onsite repulsion) ≫\gg≫ ttt (the nearest-neighbor hopping). For small electron dopings above the half-filled antiferromagnet, we numerically uncover a rich variety of magnetically ordered states, and in conjunction with theoretical arguments, infer the phase diagram of the system as a function of doping and interaction strengths. In particular, we find that the inclusion of long-range Coulomb interactions induces an instability of high-spin states$\unicode{x2014}$such as the saturated Nagaoka ferromagnet$\unicode{x2014}$towards phase separation and stripe ordering. We also present proposals for the observation of some of our key findings in experiments that would shed further light on this paradigmatic strongly correlated system.
We discuss the rich phase diagram of doped $A{B}_{2}\phantom{\rule{4pt}{0ex}}t\text{\ensuremath{-}}J$ chains by using data from density matrix renormalization group and exact diagonalization techniques. The JJJ vs $\ensuremath{\delta}$ (hole doping) phase diagram exhibits regions of itinerant ferrimagnetism, incommensurate, resonating valence bond and Nagaoka states, phase separation, and Luttinger liquid (LL) physics. Several features are highlighted, such as the modulated ferrimagnetic structure, the occurrence of Nagaoka spin polarons in the underdoped regime and small values of J=4t2/UJ=4{t}^{2}/UJ=4t2/U, where ttt is the first-neighbor hopping amplitude and UUU is the on-site repulsive Coulomb interaction, incommensurate structures with nonzero magnetization, and strong-coupling LL physics in the high-doped regime. We also verify that relevant findings are in agreement with the corresponding findings in square and nnn-leg ladder lattices. In particular, we mention the instability of Nagaoka ferromagnetism against JJJ and $\ensuremath{\delta}$.