Effects of Lorentz-symmetry violation on the spectra of rare-earth ions in a crystal field

We demonstrate that experiments measuring the transition energies of rare-earth ions doped in crystalline lattices are sensitive to violations of local Lorentz invariance and Einstein's equivalence principle. Using the crystal field of LaCl3 as an example, we calculate the frame-dependent energy shifts of the transition frequencies between low-lying states of Ce3+, Nd3+, and Er3+ dopants in the context of the standard model extension, and show that they have high sensitivity to electron anomalies that break rotational invariance.