FQHESphereExtractRootPartitions

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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.