Quantum compass model on the square lattice

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 = − r (JxσWhen Jx = Jz, 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 Jx = Jz. 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 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.

The emergence of resonating valence bond physics in spin–orbital models

“…So the Hamiltonian is only invariant if one simultaneously performs the same rotation in real space and in pseudo-spin space. For purely orbital models, this is known to have remarkable consequences [34,35,36,37]. For spin-orbital models, this implies that dimers with different orientations involve different orbital wave-functions, as can be clearly seen in phases C and C'.…”

Quantum phase transition in the quantum compass model

“…The excitation gap that separates the true ground state and other 2 L−1 low-energy excitation states collapses exponentially as the system size goes to infinity. 4 In this case, the spontaneously broken symmetries are the Z 2 symmetries of the one-dimensional Ising chain along the ordering direction. Let us consider a system L x ϫ L z and let both L x and L z increase to infinity.…”

“…This conclusion is consistent with the spin-wave analysis. 4 In spin-wave analysis, fluctuations of both directions are taken into account partially. In our approach, the most important fluctuations, namely the ordering direction of weaker bond, is solved exactly.…”

“…[2][3][4][5] It was originally proposed as a simplified model to describe some Mott insulators with orbit degeneracy described by a pseudospin. In particular, the compass model describes a system where the anisotropy of the spin coupling is related to the orientation of bonds.…”

“…The results from semiclassical spin-wave study, exact diagonalization, and Green's function Monte Carlo calculation on finite-size clusters have suggested that the system develops a spontaneously symmetry-broken state in the thermodynamic limit. 4 In the spin-wave study, the Hamiltonian is expanded around the uniform classical ground state up to the first order of 1 / S. It is found that there is a directional ordering of the ground state at the symmetric point. 4 From finite-size diagonalization of samples with size up to 5 ϫ 5 and Green's function Monte Carlo calculation for system sizes up to 16ϫ 16, it is shown that on clusters of dimension L ϫ L, the low-energy spectrum consists of 2 L states which collapse onto each other exponentially fast with L. At the symmetric point of J x = J z , 2 ϫ 2 L states collapse exponentially fast with L onto the ground state.…”