We explore the possibility to break time-reversal invariance at the junction of quantum wires. The universal features in the bulk of the wires are described by the anyon Luttinger liquid. A simple necessary and sufficient condition for the breaking of time-reversal invariance is formulated in terms of the scattering matrix at the junction. The phase diagram of a junction with generic number of wires is investigated in this framework. We give an explicit classification of those critical points, which can be reached by bosonization and study the interplay between their stability and symmetry content.

• Received 29 July 2009

DOI:https://doi.org/10.1103/PhysRevB.80.245441