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arXiv:2008.11599

Exact Plaquette-Ordered Ground States with Exact Edge States of the Generalized Hubbard Model in Corner Sharing Lattices

Naoto Nakatsuji, Satoshi Nishimoto, Nakamura, Masaaki

Published Aug 25, 2020• 0 citations
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Abstract

We discuss exact plaquette-ordered ground states of the generalized Hubbard model based on the projection operator method for several corner sharing lattices: Kagome, checkerboard, and pyrochlore lattices. The obtained exact ground states are interpreted as Néel ordered states on the plaquette-located electrons. We demonstrate that these models also have exact edge states. We also calculate the entanglement entropy exactly in these systems.

DOI
10.48550/arxiv.2008.11599

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We discuss exact plaquette-ordered ground states of the generalized Hubbard model based on the projection operator method for several corner sharing lattices: Kagome, checkerboard, and pyrochlore lattices. The obtained exact ground states are interpreted as Néel ordered states on the plaquette-located electrons. We demonstrate that these models also have exact edge states. We also calculate the entanglement entropy exactly in these systems.
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An extended Hubbard model (including nearest-neighbor repulsion and antiferromagnetic spin exchange) is investigated on the frustrated checkerboard lattice, a two-dimensional analog of the pyrochlore lattice. Combining Gutzwiller renormalized mean-field calculations, exact diagonalization techniques, and a weak-coupling renormalization group analysis we provide strong evidence for a crystalline valence bond plaquette phase at quarter-filling. The ground state is twofold degenerate and breaks translation symmetry. The bond energies show a staggering while the charge distribution remains uniform.
The checkerboard lattice, with alternating 'crossed' plaquettes, serves as the two dimensional analog of the pyrochlore lattice. The corner sharing plaquette structure leads to a hugely degenerate ground state, and no magnetic order, for classical spins with short range antiferromagnetic interaction. For the half-filled Hubbard model on this structure, however, we find that the Mott insulating phase involves virtual electronic processes that generate longer range and multispin couplings. These couplings lift the degeneracy, selecting a 'flux like' state in the Mott insulator. Increasing temperature leads, strangely, to a sharp crossover from this state to a '120 degree' correlated state and then a paramagnet. Decrease in the Hubbard repulsion drives the system towards an insulator-metal transition-the moments reduce, and a spin disordered state wins over the flux state. Near the insulator-metal transition the electron system displays a pseudogap extending over a large temperature window.
I use an improved version of the two-step density matrix renormalization group method to study ground-state properties of the 2D Heisenberg model on the checkerboard lattice. In this version the Hamiltonian is projected on a tensor product of two-leg ladders instead of chains. This allows investigations of 2D isotropic models. I show that this method can describe both the magnetically disordered and ordered phases. The ground-state phases of the checkerboard model as J2J_2J2​ increases are: (i) Néel with Q=(π,π)Q=(π,π)Q=(π,π), (ii) a valence bond crystal (VBC) of plaquettes, (iii) Néel with Q=(π/2,π)Q=(π/2,π)Q=(π/2,π), and (iv) a VBC of crossed dimers. In agreement with previous results, I find that at the isotropic point J2=J1J_2=J_1J2​=J1​, the ground state is made of weakly interacting plaquettes with a large gap Δ≈0.67J1Δ\approx 0.67 J_1Δ≈0.67J1​ to triplet excitations.