Geodesic
Ambiguity in renormalization of the~conductance of an~X-junction between quantum wires with a~Luttinger-type interaction
Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 1, pp. 57-67

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the conductance renormalization for the four-lead junction of semi-infinite wires in the scattering state formalism. We use the model of spinless fermions with a short-range Luttinger-type interaction and find the renormalization group (RG) equations for the conductances of the system in the first order of the fermionic interaction. In contrast to the well-known cases of two-lead and three-lead junctions, the four-lead case does not admit a formulation of the RG equations solely in terms of conductances. The arising ambiguity with arbitrariness in the choice of the sign of $S$-matrix elements related to identical conductance matrices might be connected with a symmetry of the particle–hole type in the Hamiltonian. We show that there are two distinct RG flows from any initial point in the space of conductances. The discovered ambiguity does not affect the scaling exponents at the fixed points.
Keywords: renormalization group, Luttinger liquid, junction, electrical conductance. 
@article{TMF_2015_185_1_a4,
     author = {D. N. Aristov and R. A. Niyazov},
     title = {Ambiguity in renormalization of the~conductance of {an~X-junction} between quantum wires with {a~Luttinger-type} interaction},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {57--67},
     publisher = {mathdoc},
     volume = {185},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a4/}
}
TY  - JOUR
AU  - D. N. Aristov
AU  - R. A. Niyazov
TI  - Ambiguity in renormalization of the~conductance of an~X-junction between quantum wires with a~Luttinger-type interaction
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2015
SP  - 57
EP  - 67
VL  - 185
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a4/
LA  - ru
ID  - TMF_2015_185_1_a4
ER  - 
%0 Journal Article
%A D. N. Aristov
%A R. A. Niyazov
%T Ambiguity in renormalization of the~conductance of an~X-junction between quantum wires with a~Luttinger-type interaction
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2015
%P 57-67
%V 185
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a4/
%G ru
%F TMF_2015_185_1_a4
D. N. Aristov; R. A. Niyazov. Ambiguity in renormalization of the~conductance of an~X-junction between quantum wires with a~Luttinger-type interaction. Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 1, pp. 57-67. http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a4/