Four-site and larger mesoscopic quantum Hall circuits exhibit interaction-driven quantum critical points with universal scaling due to relevant higher-order backscattering, while multichannel versions can restore the boundary sine-Gordon description via edge-channel looping.
Giamarchi,Quantum Physics in One Dimension (Oxford University Press, 2003)
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Tunneling in multi-site mesoscopic quantum Hall circuits
Four-site and larger mesoscopic quantum Hall circuits exhibit interaction-driven quantum critical points with universal scaling due to relevant higher-order backscattering, while multichannel versions can restore the boundary sine-Gordon description via edge-channel looping.