Low-energy effective theories of the two-thirds filled Hubbard model on the triangular necklace lattice

Abstract

Motivated by Mo${}_3$S${}_7$(dmit)${}_3$, we investigate the Hubbard model on the triangular necklace lattice at two-thirds filling. We show, using second order perturbation theory, that in the molecular limit, the ground state and the low energy excitations of this model are identical to those of the spin-one Heisenberg chain. The latter model is known to be in the symmetry protected topological Haldane phase. Away from this limit we show, on the basis of symmetry arguments and density matrix renormalization group (DMRG) calculations, that the low-energy physics of the Hubbard model on the triangular necklace lattice at two-thirds filling is captured by the ferromagnetic Hubbard-Kondo lattice chain at half filling. This is consistent with and strengthens previous claims that both the half-filled ferromagnetic Kondo lattice model and the two-thirds filled Hubbard model on the triangular necklace lattice are also in the Haldane phase. A connection between Hund's rules and Nagaoka's theorem is also discussed.

11 pages and 10 figures; typos corrected in Eqs. 8 (including parameters below this equation), 9, 10c, 14, and 31d - numerics and conclusions unaffected

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Cited by in corpus (11)

• Phase Diagram of the Spin-$1/2$ Triangular $J_1$-$J_2$ Heisenberg Model on a 3-leg Cylinder
• Topological spin liquid phase in a low-dimensional organic molecular compound
• Emergence of quasi-one-dimensional physics in Mo${}_3$S${}_7$(dmit)${}_3$, a nearly-isotropic three-dimensional molecular crystal
• Heisenberg and Dzyaloshinskii-Moriya interactions controlled by molecular packing in tri-nuclear organometallic clusters
• Magnetic end-states in a strongly-interacting one-dimensional topological Kondo insulator
• Haldane insulator protected by reflection symmetry in the doped Hubbard model on the three-legged ladder
• Spin-$0$ Mott insulator to metal to spin-$1$ Mott insulator transition in the single-orbital Hubbard model on the decorated honeycomb lattice
• Topological quantum phase transition driven by anisotropic spin-orbit coupling in trinuclear organometallic coordination crystals
• Multiple insulating phases due to the interplay of strong correlations and lattice geometry in a single-orbital Hubbard model
• Effects of anisotropy in spin molecular-orbital coupling on effective spin models of trinuclear organometallic complexes
• Topological frustration and structural balance in strongly correlated itinerant electron systems: an extension of Nagaoka's theorem