Quantum compass model on the square lattice

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=−∑_r(J_xσ_r^xσ_r+ex^x+J_zσ_r^zσ_r+ez^z). When J_x≠J_z, we show that, on clusters of dimension L×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 2×2^L. We also extend the symmetry analysis of the model to arbitrary spins and show that the twofold degeneracy of all eigenstates remains true for arbitrary half-integer spins but does not apply to integer spins, in which cases the eigenstates are generically nondegenerate, a result confirmed by exact diagonalizations in the spin-1 case. Implications for Mott insulators and Josephson junction arrays are briefly discussed.