New criticality of 1D fermions.

One-dimensional massive quantum particles (or 1 + 1-dimensional random walks) with short-ranged multi-particle interactions are studied by exact renormalization group methods. With repulsive pair forces, such particles are known to scale as free fermions. With finite m-body forces (m = 3, 4, . . .), a critical instability is found, indicating the transition to a fermionic bound state. These unbinding transitions represent new universality classes of interacting fermions relevant to polymer and membrane systems. Implications for massless fermions, e.g. in the Hubbard model, are also noted. PACS numbers: 5.70Jk, 5.40+j, 64.60Ak to appear in Phys. Rev. Lett. Interacting quantum particles moving in one spatial dimension and imaginary time offer a unifying description of most 2D fluctuating systems. The trajectories of these particles represent (streched) polymers, domain walls or interfaces, steps on surfaces, magnetic flux lines, etc. Two ensembles have to be distinguished: (a) Vicinal surfaces [1] or systems at a 2D bulk critical point (e.g. Curie point, commensurate-to-incommensurate transition [2], surface reconstruction transition [3]) contain a finite density of such lines and are described by a massless quantum field theory which is generically isotropic and conformally invariant. (b) Systems with only a finite number of directed lines are ensembles of massive particles. Such systems may exhibit critical behavior at delocalization transitions between a low-temperature dense phase and a high-temperature dilute phase [4]. In the dense phase, the lines are bound to a bundle of transversal extension ξ⊥. Their relative fluctuations are thus constrained; correlations in longitudinal direction decay on a scale ξ‖. This phase is a bound state of the quantum particles. In the dilute phase, the lines fluctuate independently; the quantum particles are in a delocalized state. As the transition temperature is approached from below, the length scales ξ‖ and ξ⊥ = ξ ζ ‖ diverge. These transitions are generically anisotropic; the roughness exponent ζ equals 1/2 for temperature-driven transitions. Examples are wetting phenomena, polymer desorption, the helix-coil transition in DNA, and unbinding transitions of biomembrane bundles [5], which have gained considerable experimental interest recently [6]. Ensembles of interacting directed lines are also important as the replica formulation of polmers in random media [7]; those in turn are intimately related to theories of nonequilibrium directed growth. This letter aims at a systematic understanding of delocalization phenomena as renormalized continuum field theories. An exact renormalization group (RG) based on the short-distance algebra of the interaction vertices [8, 9] reveals the existence of a discrete series of universality classes that represent delocalization transitions of a finite number of interacting random walks. The possible existence of analogous