From diagham
Jump to navigation Jump to search

FQHESphereL2Diagonalize diagonalizes the <math>L^2</math> operator of the sphere. Its usage is similar to QHEFermionsTwoBodyGeneric up to some minor differences. It can handle both bosons and fermions. The statistics is set through the --statistics option that can take either of the two values : bosons or fermions. The diagonalization can be done in a squeezed basis. In that case the root configuration has to be provided through a text file identical to the those used for FQHESphereJackGenerator. Here is an example for the bosonic Laughlin state with 4 particles

  ReferenceState=1 0 1 0 1 0 1

If this file is save under laughlin_n_4_2s_6.dat, one can generate the corresponding state using the property the Laughlin state is the unique densest <math>L=0</math> having this root configuration

$PATHTODIAGHAM/build/FQHE/src/Programs/FQHEOnSphere/FQHESphereL2Diagonalize -p 4 -l 6 -z 0 --statistics bosons --haldane --reference-file laughlin_n_4_2s_6.dat --use-lapack --eigenstate -n 1

-z allows to set the <math>2 L_z</math> and --haldane indicates that we are using a squeezed basis. Running this command line generates both the spectrum (bosons_l2_n_4_2s_6_lz.dat) and the groundstate (bosons_l2_n_4_2s_6_lz_0.0.vec) which is that precise case, the Laughlin state.