Fig. 5: Modifications to two-body and three-body pseudopotentials.
From: Flat bands on a spherical surface from Landau levels to giant-quantum-number orbitals
The effective pseudopotential parameters for the lth and (l + 1)th flat bands mixing with orbital angular momentum l = 12 and different strength of magnetic monopole Q, where the sphere radius for Q = 0 is the same as that for Q = l. All modifications are negative values. a \({\beta }_{1}=\mathrm{lg}\,\left| \frac{{{\mathbb{V}}}_{J}^{2{\rm{-bodym}}}-{{\mathbb{V}}}_{J}^{2{\rm{-body}}}}{{{\mathbb{V}}}_{J}^{2{\rm{-body}}}}\right| \) represents the logarithmic ratio of the modification to the two-body pseudopotential parameters, to the two-body pseudopotential parameters within a single flat band. Blue open squares, purple open diamonds, green open triangles, and Red open circles represent Q = 0, l, l − 1, and l − 2, respectively. b \({\beta }_{2}=\mathrm{lg}\,\left| \frac{{{\mathbb{V}}}_{J,\alpha }^{3{\rm{-bodym}}}}{{{\mathbb{E}}}_{J,\alpha }}\right| \) denotes the logarithmic ratio of the modification to the three-body pseudopotential parameters, to the three-electron energy \({{\mathbb{E}}}_{J,\alpha }\) from the two-body effective interaction \({\sum }_{J}{{\mathbb{V}}}_{J}^{{\rm{2-bodym}}}{\hat{{\mathbb{H}}}}_{J}^{{\rm{2-bodym}}}\). Source data are provided in the Supplementary Data.
