Determine the effective coupling C for contact interaction in the bosonic LLL Pfaffian model

Determine the quantitative value of the coupling constant C in the modified effective Hamiltonian H^{mod} that corresponds to bosons in the lowest Landau level at filling factor one with a contact (delta-function) interaction projected to the LLL. This entails identifying the value of C that appropriately models the physical two-body contact interaction within the composite-fermion mean-field framework where Pfaffian pairing appears only for C > 2.

Background

The paper introduces a modified effective Hamiltonian H^{mod} for bosons at filling factor one in the lowest Landau level by adding a term weighted by a parameter C to enforce pairing tendencies consistent with the Pfaffian state. In the self-consistent mean-field analysis, nontrivial Pfaffian solutions appear only if C exceeds a threshold (C > 2).

To connect this effective description with the physical system of bosons interacting via a contact potential projected to the LLL, the authors highlight that the precise value of C corresponding to the real interaction strength is not currently determined. Establishing this mapping is necessary to quantitatively calibrate the effective model and compare with numerical and experimental results.