Abstract
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.
Highlights
The objective of this paper is to study a local impurity coupled to a multi-channel Luttinger liquid
Our results describe an array of wires with low density of impurities at moderate temperatures when thermal length is smaller than the mean distance between impurities and, each impurity renormalises individually
The explicit expressions for the inter-wire density-density, (α±), and current-current, (α−), interactions are not universal. Their dependence on bare values of interactions and the mean particle density differ for bosons and fermions and, we will not dwell on these details
Summary
The objective of this paper is to study a local impurity coupled to a multi-channel Luttinger liquid
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