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arXiv:0709.2688

Néel and Valence-Bond Crystal phases of the Two-Dimensional Heisenberg Model on the Checkerboard Lattice

S. Moukouri

Published Sep 17, 2007• 0 citations
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Abstract

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 $J_2$ increases are: (i) Néel with $Q=(π,π)$, (ii) a valence bond crystal (VBC) of plaquettes, (iii) Néel with $Q=(π/2,π)$, and (iv) a VBC of crossed dimers. In agreement with previous results, I find that at the isotropic point $J_2=J_1$, the ground state is made of weakly interacting plaquettes with a large gap $Δ\approx 0.67 J_1$ to triplet excitations.

DOI
10.48550/arxiv.0709.2688

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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.
I use an improved version of the two-step density-matrix renormalization group method to study ground-state properties of the two-dimensional (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 J2{J}_{2}J2​ increases are (i) N\'eel with $Q=(\ensuremath{\pi},\ensuremath{\pi})$, (ii) a valence-bond crystal (VBC) of plaquettes, (iii) N\'eel with $Q=(\ensuremath{\pi}∕2,\ensuremath{\pi})$, and (iv) a VBC of crossed dimers. In agreement with previous results, I find that at the isotropic point J2=J1{J}_{2}={J}_{1}J2​=J1​, the ground state is made of weakly interacting plaquettes with a large gap $\ensuremath{\Delta}\ensuremath{\approx}0.67{J}_{1}$ to triplet excitations. The same approach is also applied to the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model. There is no evidence of a columnar dimer phase in the highly frustrated regime.
We use the recently developed tensor network algorithm based on infinite projected entangled pair states (iPEPS) to study the phase diagram of frustrated antiferromagnetic J1{J}_{1}J1​-J2{J}_{2}J2​ Heisenberg model on a checkerboard lattice. The simulation indicates a N\'eel ordered phase when J2<0.88J1{J}_{2}<0.88{J}_{1}J2​<0.88J1​, a plaquette valence bond solid state when 0.88<J2/J1<1.110.88<{J}_{2}/{J}_{1}<1.110.88<J2​/J1​<1.11, and a stripe phase when J2>1.11J1{J}_{2}>1.11{J}_{1}J2​>1.11J1​, with two first-order transitions across the phase boundaries. The calculation shows that the cross dimer state proposed before is unlikely to be the ground state of the model, although such a state indeed arises as a metastable state in some parameter region.
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