Abstract:
An effective conformal field theory (CFT) describing the low-energy excitations of a gas of spinless interacting fermions on a circle in the gapless regime (Luttinger liquid) is investigated. Functional techniques and modular-transformation properties are used to compute all correlation functions for a finite size and temperature. Forward-scattering disorder is treated exactly. Laughlin experiments on charge transport in a quantum Hall fluid on a cylinder are reviewed in this CFT framework. Edge excitations above a given bulk excitation are described by a twisted version of the Luttinger effective theory. Luttinger CFTs corresponding to the ν=1/(2p+1) filling fractions are rational CFTs (RCFT). Generators of the extended symmetry algebra are identified as edge-fermion creators and annihilators, thus giving a physical meaning to the RCFT viewpoint on edge excitations of these sequences.
Citation:
P. Degiovanni, R. Melin, K. Chaubet, “Conformal field theory approach to gapless 1D fermion systems and application to the edge excitations of ν=1/(2p+1) quantum Hall sequences”, TMF, 117:1 (1998), 5–91; Theoret. and Math. Phys., 117:1 (1998), 1113–1181
\Bibitem{DegMelCha98}
\by P.~Degiovanni, R.~Melin, K.~Chaubet
\paper Conformal field theory approach to gapless 1D fermion systems and application to the edge excitations of $\nu =1/(2p+1)$ quantum Hall sequences
\jour TMF
\yr 1998
\vol 117
\issue 1
\pages 5--91
\mathnet{http://mi.mathnet.ru/tmf918}
\crossref{https://doi.org/10.4213/tmf918}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1698525}
\zmath{https://zbmath.org/?q=an:0952.81069}
\transl
\jour Theoret. and Math. Phys.
\yr 1998
\vol 117
\issue 1
\pages 1113--1181
\crossref{https://doi.org/10.1007/BF02557158}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000078621000001}
Linking options:
https://www.mathnet.ru/eng/tmf918
https://doi.org/10.4213/tmf918
https://www.mathnet.ru/eng/tmf/v117/i1/p5
This publication is cited in the following 4 articles:
Cabra D.C., De M.artino A., Honecker A., Pujol P., Simon P., “Emergence of irrationality: Magnetization plateaus in modulated Hubbard chains”, Physical Review B, 63:9 (2001), 094406
Degiovanni, P, “Decoherence of Schrodinger cat states in a Luttinger liquid”, Physical Review B, 62:16 (2000), 10706
Da Cruz, W, “Fractons and fractal statistics”, International Journal of Modern Physics A, 15:24 (2000), 3805
Liguori, A, “Bosonization at finite temperature and anyon condensation”, Nuclear Physics B, 569:1–3 (2000), 577
Citation in format AMSBIB
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