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Motivated by recent neutron scattering experiments, we derive and study aneffective "pseudo-dipolar" spin-1/2 model for the XY pyrochlore antiferromagnetEr2Ti2O7. While a bond-dependent in-plane exchange anisotropy removes anycontinuous symmetry, it does lead to a one-parameter `accidental' classicaldegeneracy. This degeneracy is lifted by quantum fluctuations in favor of thenon-coplanar spin structure observed experimentally -- a rare experimentalinstance of quantum order by disorder. A non-Goldstone low-energy mode ispresent in the excitation spectrum in accordance with inelastic neutronscattering data. Our theory also resolves the puzzle of the experimentallyobserved continuous ordering transition, absent from previous models.

Quantum order by disorder and accidental soft mode Er2Ti2O7