Extraction of many-body Chern number from a single wave function
The quantized Hall conductivity of integer and fractional quantum Hall (IQH and FQH) states is directly related to a topological invariant, the many-body Chern number. The conventional calculation of this invariant in interacting systems requires a family of many-body wave functions parameterized by twist angles in order to calculate the Berry curvature. In this work, we demonstrate how to extract the Chern number given a single many-body wave function, without knowledge of the Hamiltonian. We perform extensive numerical simulations involving IQH and FQH states to validate these methods. We also propose an ancilla-free experimental scheme for the measurement of this invariant. Specifically, we use the statistical correlations of randomized measurements to infer the MBCN of a wavefunction.
Seminar will be held via Zoom: https://umd.zoom.us/j/97099328991 and Meeting ID : 970 9932 8991