Towards the fractional Quantum Hall Effect: a noncommutative geometry perspective

Speaker(s)

Matilde Marcolli

Affiliation

Max-Planck-Institut fuer Mathematik, Bonn

Date

Dec. 7, 2004, noon

Room

room 5810

Seminar

Seminar Algebraic Topology

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In this joint work with Varghese Mathai we propose an approach to the fractional Quantum Hall Effect within the framework of noncommutative geometry, using hyperbolic geometry to simulate electron-electron interactions. By computing the range of the higher cyclic traces on K-theory for cocompact Fuchsian groups, we determine the range of values of the Connes-Kubo Hall conductance in the discrete model of the quantum Hall effect on the hyperbolic plane. The new phenomenon that we observe in our case is that the Connes-Kubo Hall conductance has plateaux at integral multiples of a fractional valued topological invariant, namely the orbifold Euler characteristic. The set of possible fractions obtained in this model can be compared with recently available experimental data.

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