Fractional quantum Hall effect via the Grothendieck-Riemann-Roch formula

Abstract: We study the fractional quantum Hall effect on a Riemann surface of genus g traversed by a magnetic field of total flux d. The wave functions of charged particles have a semi-phenomenological description by Laughlin states. These states can be studied by methods of algebraic geometry: they form a holomorphic vector bundle over the d-th Picard group of the Riemann surface. The Chern characters of this vector bundle can be computed by the Grothendieck-Riemann-Roch formula. In a fully filled state the Chern character we obtain is compatible with the existence of a projectively flat connection on the vector bundle. In a state with quasiholes our computation implies that no such connection can exist. This is joint work with Semyon Klevtsov.

HEP - theorymathematical physicsalgebraic geometrycombinatoricsexactly solvable and integrable systems

Audience: researchers in the discipline

IBS-CGP Mathematical Physics Seminar

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