Quantum wire networks with local Z2 symmetry

Details Quantum wire networks with local Z2 symmetry Quantum wire networks with local Z2 symmetry

2005-07-15

arxiv.org/abs/cond-mat/0507376v2

Phys. Rev. B 72, 235114 (2005)

Physics

Condensed Matter

Strongly Correlated Electrons

16 pages, 9 figures, v.2 section IV D added,accepted for publication in PRB

Scientific paper

10.1103/PhysRevB.72.235114

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 ultra-localized single particle basis adapted to this local 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.

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