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 Er2Ti2O7 from inelastic neutron scattering measurements, we then show that the U(1)-degenerate states of Er2Ti2O7 are its classical ground states, and unambiguously show that quantum fluctuations break the degeneracy in a way which is confirmed by experiment. This is the first definitive observation of order-by-disorder in any material. We provide further verifiable consequences of this phenomenon, and several additional comparisons between theory and experiment.
@article{arxiv.1204.1320,
title = {Definitive Evidence for Order-by-Quantum-Disorder in Er2Ti2O7},
author = {Lucile Savary and Kate A. Ross and Bruce D. Gaulin and Jacob P. C. Ruff and Leon Balents},
journal= {arXiv preprint arXiv:1204.1320},
year = {2013}
}