Two extended versions of the 2D-Heisenberg model

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.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.

arXiv:0709.2688Sep 17, 20070 citations

Néel and valence-bond crystal phases of frustrated two-dimensional Heisenberg models

S. Moukouri

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 ${J}_{2}$ 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 ${J}_{2}={J}_{1}$ , 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.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 ${J}_{2}$ 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 ${J}_{2}={J}_{1}$, 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.

Physical Review BFeb 28, 200817 citations

Ground state of the two-dimensional antiferromagnetic Heisenberg model studied using an extended Wigner-Jordon transformation

Y. R. Wang

A two-dimensional (2D) Wigner-Jordon transformation which maps spin variables into spinless fermion variables is found and is used to study the 2D spin-1/2 antiferromagnetic Heisenberg model. The transformation generates a fictitious gauge field in the XY component of the Heisenberg model, and hence induces an in-phase orbital current in the Ising component flowing around each elementary plaquette of the underlying lattice. The ground state of the Heisenberg model in a 2D square lattice is found to be an in-phase N\'eel flux phase, i.e., a coexisting state of the flux phase with in-phase orbital currents and a long-range antiferromagnetic spin order. The zero-temperature mean-field energy of the in-phase N\'eel flux state, ${\mathit{E}}_{0}$ =-0.33J per bond, is only 1% higher than the best-estimated ground-state energy, -0.334J per bond.A two-dimensional (2D) Wigner-Jordon transformation which maps spin variables into spinless fermion variables is found and is used to study the 2D spin-1/2 antiferromagnetic Heisenberg model. The transformation generates a fictitious gauge field in the XY component of the Heisenberg model, and hence induces an in-phase orbital current in the Ising component flowing around each elementary plaquette of the underlying lattice. The ground state of the Heisenberg model in a 2D square lattice is found to be an in-phase N\'eel flux phase, i.e., a coexisting state of the flux phase with in-phase orbital currents and a long-range antiferromagnetic spin order. The zero-temperature mean-field energy of the in-phase N\'eel flux state, ${\mathit{E}}_{0}$=-0.33J per bond, is only 1% higher than the best-estimated ground-state energy, -0.334J per bond.

Physical review. B, Condensed matterFeb 1, 199192 citations

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.

{J}_{2}

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

{J}_{2}={J}_{1}

, 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.

{\mathit{E}}_{0}

=-0.33J per bond, is only 1% higher than the best-estimated ground-state energy, -0.334J per bond.