at which the stiffening is observed, given that finite temperature path-integral Monte Carlo calculations of several properties do not show a significant temperature dependence below 1 K [26]. In this context, a satisfactory explanation for the observed elastic stiffening in hcp solid $^{4}$He must involve intrinsic mobility issues. 

In summary, we employ a hybrid continuum-atomistic approach, based on the Peierls- Nabarro model and the shadow wave function formalism, to obtain direct insight into the intrinsic structural and mobility properties of dislocations in hcp solid $^{4}$He at zero temper- ature. In addition to providing key information concerning the elastic properties of this prototypical quantum crystal, the results reveal a significant lattice resistance to dislocation motion. Analyzing our results in the context of the proposed dislocation-pinning interpre- tation of the similarity between the NCRI and elastic stiffening phenomena suggests that intrinsic lattice resistance is an essential factor when it comes to the mobility of dislocations. The proposed interpretation, which entirely ignores this element, may therefore not provide a satisfactory explanation for the observed elastic stiffening in hcp solid 4 $_{He}$. 

The authors acknowledge financial support from the Brazilian agencies FAPESP, CNPq and CAPES. Part of the computations were performed at the CENAPAD high-performance computing facility at Universidade Estadual de Campinas. 

∗ Electronic address: rpessoa@ifi.unicamp.br 

† Electronic address: vitiello@unicamp.br 

‡ Electronic address: dekoning@ifi.unicamp.br 

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