Quantum wire networks with local Z2 symmetry

TL;DR

This paper investigates quantum wire networks with local Z2 symmetry under half flux quantum per loop, revealing that electron-electron interactions induce pair hopping processes that lead to a spin-density-wave state, destroying Luttinger liquid behavior.

Contribution

It introduces a new local Z2 symmetry in quantum wire networks and analyzes its effects on low-energy physics, showing the emergence of a spin-density-wave state due to pair hopping.

Findings

Pair hopping processes dominate due to electron-electron interactions.

Luttinger liquid behavior is suppressed, replaced by a spin-density-wave state.

Superconducting instability is not generated by these processes.

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 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.