Exact diagonalization for spin-1/2 spin ice pyrochlores

Abstract

We find exact solutions to the Hamiltonian of a 16-site spin-1/2 pyrochlore crystal with nearest neighbour exchange interactions. The methods of group theory (symmetry) are used to completely block-diagonalize the Hamiltonian, yielding precise details about symmetry of the eigenstates, in particular those components which are {\em spin ice} states, in order to evaluate the spin ice density at finite temperature. At low enough temperatures, a `perturbed' spin ice phase is clearly outlined within the four parameter space of the general model of exchange interactions. The quantum spin ice phase is expected to exist outside these boundaries.