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arXiv:cond-mat/0507376 · Physical Review B

Quantum wire networks with local Z2 symmetry

K. Kazymyrenko, Sébastien Dusuel, Benoît Douçot

Published Dec 19, 2005• 6 citations
arXivHTMLPDF

Abstract

For a large class of networks made of connected loops, in the presence of an external magnetic field of half flux quantum per loop, we show the existence of a large local symmetry group, generated by simultaneous flips of the electronic current in all the loops adjacent to a given node. Using an ultralocalized single particle basis adapted to this local ${\mathbb{Z}}_{2}$ symmetry, we show that it is preserved by a large class of interaction potentials. As a main physical consequence, the only allowed tunneling processes in such networks are induced by electron-electron interactions and involve a simultaneous hop of two electrons. Using a mean-field picture and then a more systematic renormalization-group treatment, we show that these pair-hopping processes do not generate a superconducting instability, but they destroy the Luttinger liquid behavior in the links, giving rise at low energy to a strongly correlated spin-density-wave state.

DOI
10.1103/physrevb.72.235114

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For a large class of networks made of connected loops, in the presence of an external magnetic field of half flux quantum per loop, we show the existence of a large local symmetry group, generated by simultaneous flips of the electronic current in all the loops adjacent to a given node. Using an ultralocalized single particle basis adapted to this local Z2{\mathbb{Z}}_{2}Z2​ symmetry, we show that it is preserved by a large class of interaction potentials. As a main physical consequence, the only allowed tunneling processes in such networks are induced by electron-electron interactions and involve a simultaneous hop of two electrons. Using a mean-field picture and then a more systematic renormalization-group treatment, we show that these pair-hopping processes do not generate a superconducting instability, but they destroy the Luttinger liquid behavior in the links, giving rise at low energy to a strongly correlated spin-density-wave state.
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