Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2008-01-25
New Journal of Physics 10, 045012 (2008)
Physics
Condensed Matter
Strongly Correlated Electrons
25 pages, accepted for publication in NJP, remarks added on the poor man's RG treatment of the Y-junction and the Breit-Wigner
Scientific paper
10.1088/1367-2630/10/4/045012
We compare two fermionic renormalization group methods which have been used to investigate the electronic transport properties of one-dimensional metals with two-particle interaction (Luttinger liquids) and local inhomogeneities. The first one is a poor man's method setup to resum ``leading-log'' divergences of the effective transmission at the Fermi momentum. Generically the resulting equations can be solved analytically. The second approach is based on the functional renormalization group method and leads to a set of differential equations which can only for certain setups and in limiting cases be solved analytically, while in general it must be integrated numerically. Both methods are claimed to be applicable for inhomogeneities of arbitrary strength and to capture effects of the two-particle interaction, such as interaction dependent exponents, up to leading order. We critically review this for the simplest case of a single impurity. While on first glance the poor man's approach seems to describe the crossover from the ``perfect'' to the ``open chain fixed point'' we collect evidence that difficulties may arise close to the ``perfect chain fixed point''. Due to a subtle relation between the scaling dimensions of the two fixed points this becomes apparent only in a detailed analysis. In the functional renormalization group method the coupling of the different scattering channels is kept which leads to a better description of the underlying physics.
Andergassen Sabine
Enss Tilman
Meden Volker
Schoeller Harry
Schoenhammer Kurt
No associations
LandOfFree
Fermionic renormalization group methods for transport through inhomogeneous Luttinger liquids does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Fermionic renormalization group methods for transport through inhomogeneous Luttinger liquids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fermionic renormalization group methods for transport through inhomogeneous Luttinger liquids will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-412263