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Quantum wetting transitions in two dimensions: an alternative path to non-universal interfacial singularities

We consider two-dimensional ($d=2$) systems with short-ranged microscopic interactions, where interface unbinding (wetting) transitions occur in the limit of vanishing temperature $T$. For $T=0$ the transition is characterized by non-universal critical properties analogous to those established for thermal wetting transitions in $d=3$, albeit with a redefined capillary parameter $\tildeω$. Within a functional renormalization-group treatment of an effective interfacial model, we compute the finite temperature phase diagram, exhibiting a line of interface unbinding transitions, terminating at $T=0$ with an interfacial quantum critical point. At finite $T$ we identify distinct scaling regimes, reflecting the interplay between quantum and thermal interfacial fluctuations. A crossover line marking the onset of the quantum critical regime is described by the $d=3$ interfacial correlation-length exponent $ν_{||}$. This opens a new way to investigate the non-universal character of $ν_{||}$ without penetrating the true critical regime. On the other hand, the emergent interfacial quantum critical regime shows no signatures of non-universality.