Quantum dissociation of an edge of a Luttinger liquid
  In a Luttinger liquid phase of one-dimensional molecular matter the strength of zero-point motion can be characterized by dimensionless De Boer's number quantifying the interplay of quantum fluctuations and two-body interactions. Selecting the latter in the Morse form we show that dissociation of the Luttinger liquid is a process initiated at the system edge. The latter becomes unstable against quantum fluctuations at a value of De Boer's number which is smaller than that of the bulk instability which parallels the classical phenomenon of surface melting. 
Eugene B. Kolomeisky and Michael Timmins