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arXiv:2208.05899 · Physical Review A

Ferromagnetism in the SU( N ) Kondo lattice model: SU( N ) double exchange and supersymmetry

Keisuke Totsuka

Published Mar 17, 2023• 13 citations
arXivHTMLPDF

Abstract

We study the ground-state properties of the SU($N$) generalization of the Kondo lattice model in one dimension when the Kondo coupling ${J}_{\text{K}}$ (both ferromagnetic and antiferromagnetic) is sufficiently strong. Both cases can be realized using alkaline-earth-metal-like cold gases in optical lattices. Specifically, we first carry out the strong-coupling expansion and identify two insulating phases [one of which is the SU($N$) analog of the well-known gapped Kondo singlet phase]. We then rigorously establish that the ground state in the low-density (for ${J}_{\text{K}}<0$) or the high-density (for ${J}_{\text{K}}>0$) region is ferromagnetic. The results are accounted for by generalizing the double-exchange mechanism to SU($N$) ``spins.'' Possible realizations of Bose-Fermi supersymmetry SU($N|1$) in the (generalized) SU($N$) Kondo lattice model are discussed as well.

DOI
10.1103/physreva.107.033317

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We study higher-spin ($S\ensuremath{\ge}1$) generalization of the one-dimensional Kondo-Heisenberg model, in which the local spin-SSS moments of the Kondo-lattice model interact with each other via the antiferromagnetic Heisenberg interaction (JH{J}_{\text{H}}JH​), by analytical and numerical methods. The strong-coupling (i.e., large Kondo coupling) expansion maps out an insulating phase at half-filling whose magnetic correlation depends on the parity of 2S2S2S as well as a ferromagnetic metallic phase which dominates the strong-coupling region at generic fillings. Then, we carried out the density-matrix renormalization-group simulations for S=1S=1S=1 to closely investigate the phase structure at large but finite Kondo coupling. At half-filling, the Kondo coupling and JH{J}_{\text{H}}JH​ do not compete and the insulating spin-gapless phase is stable, while the competition of the two leads to a stepwise collapse of the strong-coupling ferromagnetism via an intervening dimerized insulating phase with power-law spin correlation at quarter-filling.
Abstract We develop a general theory of flat-band ferromagnetism in the SU(N) Fermi–Hubbard model, which describes the behavior of N-component fermions with SU(N) symmetric interactions. We focus on the case where the single-particle spectrum has a flat band at the bottom and establish a necessary and sufficient condition for the SU(N) Hubbard model to exhibit ferromagnetism when the number of particles is the same as the degeneracy. We show that the occurrence of ferromagnetism is equivalent to the irreducibility of the projection matrix onto the space of single-particle ground states. We also demonstrate that this result can be exploited to establish a rigorous result for the ferromagnetic SU(N) Kondo lattice model with a flat band. Specifically, we prove that when the SU(N) Hubbard model is ferromagnetic, the ferromagnetic SU(N) Kondo lattice model with the same hopping matrix also exhibits SU(N) ferromagnetism.
Using a non-Abelian density matrix renormalization group method we determine the phase diagram of the Kondo lattice model in one dimension, by directly measuring the magnetization of the ground state. This allowed us to discover a second ferromagnetic phase missed in previous approaches. The phase transitions are found to be continuous. The spin-spin correlation function is studied in detail, and we determine in which regions the large and small Fermi surfaces dominate. The importance of double-exchange ordering and its competition with Kondo singlet formation is emphasized in understanding the complexity of the model.
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The exact and analytical low energy spectrum of the ferromagnetic Kondo lattice model on a complete graph extended with on-site repulsion UUU is obtained in terms of a dynamical spl(2,1) supersymmetry in the limit of infinitely strong Hund's coupling (double exchange). Furthermore, we show that for the particular value of U=JH/2U=J_H/2U=JH​/2 the supersymmetry is not constrained to infinite JH/tJ_H/tJH​/t only and we calculate the energy including the t2/JHt^2/J_Ht2/JH​ corrections analytically and we give numerical evidence which suggest that the Kondo Hamiltonian is itself supersymmetric for any JH/tJ_H/tJH​/t. On a NNN site graph, the ferromagnetic ground state is realized for 1 and NNN+1 electrons only. In the leading order in the value of the core spin, the quantum and semiclassical spectra are identical.