  Inspired by the recent work [MRT21], we prove a non-universal non-central
Moderate Deviation principle for the nodal length of arithmetic random waves
(Gaussian Laplace eigenfunctions on the standard flat torus) both on the whole
manifold and on shrinking toral domains. Second order fluctuations for the
latter were established in [MPRW16] and [BMW20] respectively, by means of
chaotic expansions, number theoretical estimates and full correlation
phenomena. Our proof is simple and relies on the interplay between the long
memory behavior of arithmetic random waves and the chaotic expansion of the
nodal length, as well as on well-known techniques in Large Deviation theory
(the contraction principle and the concept of exponential equivalence).
