Abstract
The effective action for low-energy excitations of Laughlin's states is obtained by systematic expansion in inverse powers of the magnetic field. It is based on the W-infinity symmetry of quantum incompressible fluids and the associated higher-spin fields. Besides reproducing the Wen and Wen-Zee actions and the Hall viscosity, this approach further indicates that the low-energy excitations are extended objects with dipolar and multipolar moments.
Highlights
We present the basic features of the W∞ symmetry on the edge and in the bulk; we set up the /B0 expansion and introduce the associated higher-spin hydrodynamic fields
We conclude that the W∞ symmetry of the incompressible fluid in the lowest Landau level shows the existence of non-local fluctuations, that can be made local by expanding in powers of 1/B0 and introducing a generalized hydrodynamic approach with higher-spin traceless symmetric fields
We have found that the W∞ symmetry of incompressible fluids led to introduce a spin-two hydrodynamic field, whose coupling to the metric induces the Wen-Zee action, earlier obtained by coupling the spin connection to the charge current (cf. eq (2.8))
Summary
This is S = 2s; upon comparing with the actual expression of the Laughlin wave function in this geometry, one obtains the value of the intrinsic angular momentum s = 1/2ν = p/2 [16] The shift is another universal quantum number characterizing Hall states, besides Wen’s topological order [40], that depends on the topology of space. Upon using these formulas, we approximate the Wen-Zee action to quadratic order in the fluctuations of both gravity and electromagnetic backgrounds, and obtain: νs SWZ = 4π From this expression, we can compute the induced stress tensor to leading order in the metric and for constant magnetic field B(x) = B0, leading to the result:. The Jain hierarchy of fractional Hall states was uniquely derived by assuming this symmetry and the minimality of the spectrum of excitations [33,34,35]
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