FQHESphereExtractRootPartitions
FQHESphereExtractRootPartitions extracts admissible configurations (i.e. root configurations) from a set of eigenstates. It can be used in two different ways. As an example, let's generate some quasihole states of the Halperin (332) phase using FQHESphereFermionsWithSpin
$PATHTODIAGHAM/build/FQHE/src/Programs/FQHEOnSphere/FQHESphereFermionsWithSpin -p 6 -l 13 --interaction-name halperin_332 --nbr-lz 2 --use-lapack --interaction-file pseudopotentials_332_2s_13.dat --full-diag 8000 -n 20 --eigenstate
where we input the pseudo-potential file pseudopotentials_332_2s_13.dat
Pseudopotentials = 1 1 0 0 0 0 0 0 0 0 0 0 0 0
We get 7 quasihole states at <math>S_z=0</math>, 4 in the <math>L_z=0</math> sectors and 3 in the <math>L_z=1</math> sectors. Now providing the spectrum to FQHESphereExtractRootPartitions
$PATHTODIAGHAM/build/FQHE/src/Programs/FQHEOnSphere/FQHESphereExtractRootPartitions fermions_sphere_su2_halperin_332_n_6_2s_13_sz_0_lz.dat
will produce a file fermions_sphere_su2_halperin_332_n_6_2s_13_sz_0_lz.root that contains the root configurations of the 7 states
total nbr of root partitions : 10 nbr of root partitions per Lz sector : 4 3 ----------------------------------------- Lz = 0 : d 0 u 0 0 d 0 0 u 0 0 d 0 u d 0 u 0 0 u 0 0 d 0 0 d 0 u d 0 0 d 0 u 0 0 d 0 u 0 0 u u 0 0 d 0 u 0 0 d 0 u 0 0 d nbr states = 4 ----------------------------------------- Lz = 1 : d 0 u 0 0 0 d 0 u 0 0 d 0 u d 0 0 d 0 u 0 0 u 0 0 d 0 u u 0 0 d 0 u 0 0 d 0 0 d 0 u nbr states = 3 -----------------------------------------
The first line gives the total number of states, assuming the spectrum is <math>L_z \leftrightarrow -L_z</math> symmetric (so here 4+3+3=10). The third line gives the number of quasihole states per positive <math>L_z</math> sector. Then for each <math>L_z</math> sector, we obtain the root configurations.
Instead of providing an energy spectrum, we can provide a list of states via the --eigenstate-list option. This option uses a single column text file that lists all the states that have to be considered.