# FQHE programs

These are all the available programs in DiagHam that are related to the Fractional Quantum Hall Effect

## Basic usage

FQHESphereCP2GenericInteraction allows one to diagonalize any two-body interaction in the lowest Landau level of the CP2 geometry. The generic use is:

\$PATHTODIAGHAM/build/FQHE/src/Programs/FQHEOnSphere/FQHESphereCP2GenericInteraction -p 2 -l 3 --interaction-name V1 --interaction-file pseudopotential_v1.dat --use-lapack

The form of the interaction is defined in an ASCII file provided in the --interaction-file option. It specifies the value of all two-body pseudopotentials. It should contain one line of the form:

   Pseudopotentials = 0 1


One also has to provide the list of all Clebsch-Gordan coefficients necessary for the composition of SU(3) momenta. A particle in the lowest Landau level of the CP2 geometry is in a (N_{\phi},0) SU(3) representation, where (p,0) \otimes (p,0) = \oplus_{p' = 0}^{p} \left( 2(p - p'), p' \right)

This will diagonalize the coulomb interaction in each Lz sectors. Option -p sets the number of particles and -l the one-body maximum angular momentum (which matches the number of flux quanta in the lowest Landau level). Running this command produces one file named fermions_cp2_V1_n_2_2s_3.dat that looks like :

   # tz y E
1 -9 1
0 -6 1
0 -6 1
2 -6 1
1 -3 2.2204460492503e-16
1 -3 1
1 -3 1
0 0 -6.1309083055668e-31
0 0 1
0 0 1
3 -3 1.1102230246252e-16
3 -3 1
...


This a three-column ASCII file. The first column is the tz sector (rounded to the closest lower integer), the second column is the y sector and the third column is the energies sorted from the lowest to the highest. The name of the interaction appearing in the output file is set using the --interaction-name option.