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We show that the Fractional Quantum Hall Effect can be phenomenologically described as a special flow of a quantum incompressible Euler liquid.
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In equivalent form condition ( 21
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A similar shift of velocity has been also observed in hydrodynamics of Calogero model A.G.Abanov, P. Wiegmann, Phys.Rev.Lett. 95:076402 (2005); E.Bettelheim, A.G.Abanov, P.B. Wiegmann, ibid 97:246401(2006); M.Stone et al J.Phys.A 41:275401 (2008)
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A similar equation but with the term − 1 4 π ν Δ log ρ -\frac{1}{4\pi}\nu\Delta\log\rho instead of the term 1 4 π ( 1 2 − ν ) Δ log ρ \frac{1}{4\pi}(\frac{1}{2}-\nu)\Delta\log\rho follows from the effective action of Kivelson ; Read89 . That approach misses the shift contribution erroneously featuring the wrong sign of the correction
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A.G. Abanov, J. Phys. A: Math. Theor. 46 (2013) 292001
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