The Quantum Compass Model on the Square Lattice

J. Dorier; F. Becca; F. Mila

doi:10.1103/PhysRevB.72.024448

paper

The Quantum Compass Model on the Square Lattice

arXiv:cond-mat/0501708 · doi:10.1103/PhysRevB.72.024448

Abstract

Using exact diagonalizations, Green's function Monte Carlo simulations and high-order perturbation theory, we study the low-energy properties of the two-dimensional spin-1/2 compass model on the square lattice defined by the Hamiltonian $H = - \sum_{r} (J_{x} σ_{r}^{x} σ_{r + e_{x}}^{x} + J_{z} σ_{r}^{z} σ_{r + e_{z}}^{z})$ . When $J_{x} \neq = J_{z}$ , we show that, on clusters of dimension $L \times L$ , the low-energy spectrum consists of $2^{L}$ states which collapse onto each other exponentially fast with $L$ , a conclusion that remains true arbitrarily close to $J_{x} = J_{z}$ . At that point, we show that an even larger number of states collapse exponentially fast with $L$ onto the ground state, and we present numerical evidence that this number is precisely $2 \times 2^{L}$ . We also extend the symmetry analysis of the model to arbitrary spins and show that the two-fold degeneracy of all eigenstates remains true for arbitrary half-integer spins but does not apply to integer spins, in which cases eigenstates are generically non degenerate, a result confirmed by exact diagonalizations in the spin-1 case. Implications for Mott insulators and Josephson junction arrays are briefly discussed.

8 pages, 8 figures

The Quantum Compass Model on the Square Lattice

Abstract

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