Title: Edge states in non-Fermi liquids,
Abstract: We devise an approach to the calculation of scaling dimensions of generic
operators describing scattering within multi-channel Luttinger liquid. The
local impurity scattering in an arbitrary configuration of conducting and
insulating channels is investigated and the problem is reduced to a single
algebraic matrix equation. In particular, the solution to this equation is
found for a finite array of chains described by Luttinger liquid models. It is
found that for a weak inter-chain hybridisation and intra-channel
electron-electron attraction the edge wires are robust against disorder whereas
bulk wires, on contrary, become insulating. Thus, the edge state may exist in a
finite sliding Luttinger liquid without time-reversal symmetry breaking
(quantum Hall systems) or spin-orbit interaction (topological insulators).