Dislocations are shown to be smooth at zero temperature because of the effective Coulomb-type interaction between kinks. Crossover to finite temperature rougnehing is suggested to be a mechanism responsible for the softening of he4 shear modulus rece
ntly observed by Day and Beamish (Nature, {bf 450}, 853 (2007)). We discuss also that strong suppresion of superfuidity along the dislocation core by thermal kinks can lead to locking in of the mechanical and superfluid responses.
Monte Carlo simulations of the SU(2)-symmetric deconfined critical point action reveal strong violations of scale invariance for the deconfinement transition. We find compelling evidence that the generic runaway renormalization flow of the gauge coup
ling is to a weak first order transition, similar to the case of U(1)$times$U(1) symmetry. Our results imply that recent numeric studies of the N`{e}el antiferromagnet to valence bond solid quantum phase transition in SU(2)-symmetric models were not accurate enough in determining the nature of the transition.
We comment on the claim of continuous phase transition in the SU(2) symmetric Deconfined Critical Point action made by O.Motrunich and A.Vishwanath in ArXive:0805.1494
On the basis of first-principle Monte Carlo simulations we find that the screw dislocation along the hexagonal axis of an hcp He4 crystal features a superfluid core. This is the first example of a regular quasi-one-dimensional supersolid, and one of
the cleanest cases of a regular Luttinger-liquid system. In contrast, the same type of screw dislocation in solid Hydrogen is insulating.
