6 research outputs found
Interaction-induced edge states in anisotropic non-Fermi liquids
We devise an approach to calculation of scaling dimensions of generic operators describing scattering within multi-channel Luttinger liquid. The local impurity scattering in arbitrary configuration of conducting and insulating channels is investigated and the problem is reduced to a single algebraic matrix equation. The application to a semi-infinite array of chains described by Luttinger liquid models demonstrates that for a weak inter-chain hybridisation and intra-channel electron-electron attraction the edge wire is robust against disorder whereas bulk wires, on contrary, become insulating in some region of inter-chain interaction parameters. This result proves that the edge states may exist in disordered anisotropic strongly correlated systems without time-reversal symmetry breaking or spin-orbit interaction and provide quantized low-temperature transport
Nonlinear Sigma Model for Disordered Media: Replica Trick for Non-Perturbative Results and Interactions
In these lectures, given at the NATO ASI at Windsor (2001), applications of
the replicas nonlinear sigma model to disordered systems are reviewed. A
particular attention is given to two sets of issues. First, obtaining
non-perturbative results in the replica limit is discussed, using as examples
(i) an oscillatory behaviour of the two-level correlation function and (ii)
long-tail asymptotes of different mesoscopic distributions. Second, a new
variant of the sigma model for interacting electrons in disordered normal and
superconducting systems is presented, with demonstrating how to reduce it,
under certain controlled approximations, to known ``phase-only'' actions,
including that of the ``dirty bosons'' model.Comment: 25 pages, Proceedings of the NATO ASI "Field Theory of Strongly
Correlated Fermions and Bosons in Low - Dimensional Disordered Systems",
Windsor, August, 2001; to be published by Kluwe