Geometric adiabatic transport in quantum Hall states

Abstract

We argue that in addition to the Hall conductance and the nondissipative component of the viscous tensor, there exists a third independent transport coefficient, which is precisely quantized. It takes constant values along quantum Hall plateaus. We show that the new coefficient is the Chern number of a vector bundle over moduli space of surfaces of genus 2 or higher and therefore cannot change continuously along the plateau. As such, it does not transpire on a sphere or a torus. In the linear response theory, this coefficient determines intensive forces exerted on electronic fluid by adiabatic deformations of geometry and represents the effect of the gravitational anomaly. We also present the method of computing the transport coefficients for quantum Hall states.

6 pages, discussion of angular momentum formulas in sec. 7 is amended

References in corpus (6)

• Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
• Density-curvature response and gravitational anomaly
• Large N expansion for the 2D Dyson gas
• Topological central charge from Berry curvature: gravitational anomalies in trial wavefunctions for topological phases
• Lorentz shear modulus of a two-dimensional electron gas at high magnetic field
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