Order by Quantum Disorder in Er2Ti2O7

Here we establish the systematic existence of a U(1) degeneracy of all symmetry-allowed Hamiltonians quadratic in the spins on the pyrochlore lattice, at the mean-field level. By extracting the Hamiltonian of Er(2)Ti(2)O(7) from inelastic neutron scattering measurements, we then show that the U(1)-degenerate states of Er(2)Ti(2)O(7) are its classical ground states, and unambiguously show that quantum fluctuations break the degeneracy in a way …