The method of separability, introduced by Symanzik,is applied in order to describe the effect of a boundary for a fractional quantum Hall liquid in the Laughlin series. An Abelian Chern-Simons theory with plane boundary is considered and the Green functions both in the bulk and on the edge are constructed, following a rigorous, perturbative, quantum field theory treatment. We show that the conserved boundary currents find an explicit interpretation in terms of the continuity equation with the electron density satisfying the Tomonaga-Luttinger commutation relation.
Symanzik's method applied to fractional quantum Hall edge states
BLASI, ALBERTO;FERRARO, DARIO;MAGGIORE, NICOLA;MAGNOLI, NICODEMO;SASSETTI, MAURA
2008-01-01
Abstract
The method of separability, introduced by Symanzik,is applied in order to describe the effect of a boundary for a fractional quantum Hall liquid in the Laughlin series. An Abelian Chern-Simons theory with plane boundary is considered and the Green functions both in the bulk and on the edge are constructed, following a rigorous, perturbative, quantum field theory treatment. We show that the conserved boundary currents find an explicit interpretation in terms of the continuity equation with the electron density satisfying the Tomonaga-Luttinger commutation relation.
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