Seminar

The generalization of the quantum Hall effect to higher dimensions is mathematically and theoretically interesting (with possible connections to noncommutative geometry), but has also become experimentally viable using the idea of synthetic dimensions. I will present the formulation of higher dimensional QHE on complex projective spaces and derive the effective actions describing the edge/bulk dynamics and the responses to changes in the external gauge and gravitational fields (related to the Hall conductivity, Hall viscosity, etc.). I will also discuss the calculation of the entanglement entropy for such systems. In the case of the lowest Landau level, a semi classical analysis shows that the entanglement entropy is proportional to the phase-space area of the entangling surface with a universal overall constant, which is the same for any dimension and for any background magnetic field.