Superclimbing modes in transverse quantum fluids: signature statistical and dynamical features

Superclimbing modes are hallmark degrees of freedom of transverse quantum fluids describing wide superfluid one-dimensional interfaces and/or edges with negligible Peierls barrier. We report the first direct numeric evidence of quantum shape fluctuations -- caused by superclimbing modes -- in simple lattice models, as well as at the free edge of an incomplete solid monolayer of $^4$He adsorbed on graphite. Our data unambiguously reveals the defining feature of the superclimbing modes -- canonical conjugation of the edge displacement field to the field of superfluid phase -- and its unexpected implication, i.e., that superfluid stiffness can be inferred from density snapshots.