Interaction Corrections to Chern Numbers

Chern numbers play a key role in many areas in physics as they describe the topology of a quantum state. Motivated by the recent experiment by Ian Speilman’s group at NIST (arXiv:1610.06228) on the second Chern number $C_2$ of the Yang monopole, we have studied the effect of particle interaction. We show that interaction will stretch the monopole into an extended manifold of singularity, which will cause a gradual change of the second Chern number as the monopole leaves the 4D surface where $C_2$ is calculated. Such gradual change is in fact contained in the data of the NIST experiment.