Determine the effect of the composite-fermion current correction

Estimate how the additional Chern–Simons contribution to the current operator, arising when a composite fermion moves while dragging its attached flux, modifies composite-fermion edge-state optical matrix elements beyond the mean-field approximation.

Background

The optical response calculation uses the mean-field current operator, but the Chern–Simons formulation of composite-fermion theory contains an additional current contribution associated with the motion of a composite fermion and its attached flux.

The paper leaves unresolved the quantitative effect of this term on edge-state dipole and current matrix elements. The authors note that addressing it would require a treatment beyond mean field, such as exact diagonalization of small systems.

References

Estimating its effect on the edge-state matrix elements would require going beyond mean-field, for example through exact diagonalization of small systems, and is left to future work.

— Optical spectroscopy of composite fermion edge states in the fractional quantum Hall effect  (2608.26521 - Sebastian et al., 27 Aug 2026) in Section 5, “Discussion and Limitations,” subsection “Correction to the current operator”