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arXiv:2209.05398

High-temperature kinetic magnetism in triangular lattices

Ivan Morera, Márton Kanász-Nagy, Tomasz Smoleński, Livio Ciorciaro, Ataç İmamoğlu, Eugene Demler

Published Sep 12, 2022• 6 citations
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Abstract

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, $U\gg t$ 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 $ν=1$, 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.

DOI
10.3929/ethz-b-000615225

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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.
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.
Kinetic-to-magnetic frustration crossover and linear confinement in the doped triangular t−Jt-Jt−J model
Microscopically understanding competing orders in strongly correlated systems is a key challenge in modern quantum many-body physics. For example, the study of magnetic polarons and their relation to pairing in the Fermi-Hubbard model in different geometries remains one of the central questions, and may help to understand the mechanism underlying unconventional superconductivity in cuprates or transition metal dichalcogenides. With recent advances in analog quantum simulation of the Fermi-Hubbard model on non-bipartite lattices, frustrated physics can now be explored experimentally in systems lacking particle-hole symmetry. Here, we study the singly doped t−Jt-Jt−J model on the triangular lattice, focusing on the competition between kinetic and magnetic frustration as a function of temperature. In doublon doped systems, we uncover a crossover between Nagaoka-type ferromagnetic (FM) correlations at high temperature and exchange mediated antiferromagnetic (AFM) order around the doublon at low temperature. For hole doped systems, kinetic Haerter-Shastry-type AFM at high temperature as well as exchange interactions at low temperature favor 120∘120^{\circ}120∘ order, strengthening magnetic correlations compared to the undoped system. In the ground state, the presence of AFM correlations throughout a wide range of interactions indicates confinement of both types of dopants. In this regime we firmly establish the presence of linear confining potentials via energy scaling arguments, supporting the picture of geometric strings in the frustrated triangular t−Jt-Jt−J model.
Microscopically understanding competing orders in strongly correlated systems is a key challenge in modern quantum many-body physics. For example, the study of magnetic polarons and their relation to pairing in the Fermi-Hubbard model in different geometries remains one of the central questions, and may help to understand the mechanism underlying unconventional superconductivity in cuprates or transition metal dichalcogenides. With recent advances in analog quantum simulation of the Fermi-Hubbard model on nonbipartite lattices, frustrated physics can now be explored experimentally in systems lacking particle-hole symmetry. Here, we study the singly doped $t\ensuremath{-}J$ model on the triangular lattice, focusing on the competition between kinetic and magnetic frustration as a function of temperature. In doublon doped systems, we uncover a crossover between Nagaoka-type ferromagnetic (FM) correlations at high temperature and exchange mediated antiferromagnetic (AFM) order around the doublon at low temperature. For hole-doped systems, kinetic Haerter-Shastry-type AFM at high temperature as well as exchange interactions at low temperature favor ${120}^{\ensuremath{\circ}}$ order, strengthening magnetic correlations compared to the undoped system. In the ground state, the presence of AFM correlations throughout a wide range of interactions indicates confinement of both types of dopants. In this regime we firmly establish the presence of linear confining potentials via energy scaling arguments, supporting the picture of geometric strings in the frustrated triangular $t\ensuremath{-}J$ model.
Quantum simulations with ultracold fermions in triangular optical lattices have recently emerged as a new platform for studying magnetism in frustrated systems. Experimental realizations of the Fermi Hubbard model revealed striking contrast between magnetism in bipartite and triangular lattices. In bipartite lattices magnetism is strongest at half filling, and doped charge carriers tend to suppress magnetic correlations. In triangular-type lattices for large U/t and t>0, antiferromagnetism (ferromagnetism) gets enhanced by doping away from n=1 with holes (doublons) because kinetic energy of dopants can be lowered through developing magnetic correlations, corresponding to formation of magnetic polarons. Snapshots of many-body states obtained with quantum gas microscopes demonstrated existence of magnetic polarons by revealing the magnetic correlations around dopants at temperatures that considerably exceed superexchange energy scale. In this paper we discuss theoretically that additional insight into properties of magnetic polarons in triangular lattices can be achieved using spectroscopic experiments with ultracold atoms. We consider starting from a spin polarized state with small hole doping and applying a two-photon Raman photoexcitation, which transfers atoms into a different spin state. We show that such magnon injection spectra exhibit a separate peak corresponding to formation of a bound state between a hole and a magnon. This polaron peak is separated from the simple magnon spectrum by energy proportional to single particle tunneling and can be easily resolved with currently available experimental techniques. For some momentum transfer there is an additional peak corresponding to photoexciting a bound state between two holes and a magnon. We point out that in two component Bose mixtures in triangular lattices one can also create dynamical magnetic polarons, with one hole and one magnon forming a repulsive bound state.
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.
Quantum simulations with ultracold fermions in triangular optical lattices have recently emerged as a new platform for studying magnetism in frustrated systems. Experimental realizations of the Fermi Hubbard model revealed striking contrast between magnetism in bipartite and triangular lattices. In bipartite lattices magnetism peaks at half filling, and doped charge carriers tend to suppress magnetic correlations. In triangular lattices for large U/tU/tU/t, magnetism is enhanced by doping away from n=1n=1n=1 because kinetic energy of dopants can be lowered through developing magnetic correlations. This corresponds to formation of magnetic polarons, with hole and doublon doping resulting in antiferro- and ferromagnetic polarons respectively. Snapshots obtained with quantum gas microscopes revealed formation of magnetic polarons around dopants at temperatures exceeding the superexchange energy scale. In this work we discuss theoretically that additional insight into properties of magnetic polarons can be achieved using spectroscopic experiments with ultracold atoms. We consider starting from a spin polarized state with small hole doping and applying a two-photon Raman photoexcitation, which transfers atoms into a different spin state. We show that such magnon injection spectra exhibit a separate peak corresponding to formation of a bound state between a hole and a magnon. This polaron peak is separated from the simple magnon spectrum by energy proportional to single particle tunneling and can be easily resolved with currently available experimental techniques. For some momentum transfer there is an additional peak corresponding to photoexciting a bound state between two holes and a magnon. We point out that in two component Bose mixtures in triangular lattices one can also create dynamical magnetic polarons, with one hole and one magnon forming a repulsive bound state.