Y-junction connecting Luttinger liquids: fixed point structure and conductances

Details Y-junction connecting Luttinger liquids: fixed point structure and conductances Y-junction connecting Luttinger liquids: fixed point structure and conductances

2011-05-30

arxiv.org/abs/1105.5883v2

Phys. Rev. B 84, 155426 (2011)

Physics

Condensed Matter

Strongly Correlated Electrons

17 pages, 4 figures. final version: extended discussion, new appendix

Scientific paper

10.1103/PhysRevB.84.155426

We study the transport properties of three Luttinger liquid wires (with possibly different interaction strength), connected through a Y-junction, within the scattering state formalism. We first formulate the problem in current algebra language and focus on the case of a symmetric set-up, for which the scattering matrix and the matrix of conductances is parametrized by two variables. For these we derive coupled RG equations, first in a ladder summation up to infinite order in the interaction. The fixed point structure and the implicit solution of these equations is presented. It is shown that higher order terms beyond the ladder approximation do not change the scaling behavior near the fixed points. For sufficiently strong attractive interaction a new fixed point with unusual properties is found.

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