FQHECylinderDensity

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FQHECylinderDensity computes the density profile and the integrated charge for states on the cylinder geometry.

First we generate the Laughlin state <math>\nu=1/3<math> using FQHESphereJackGenerator $PATHTODIAGHAM/build/FQHE/src/Programs/FQHEOnSphere/FQHESphereJackGenerator --reference-file laughlin3_n_8_2s_21.dat --fermion -o fermions_unnormalized_haldane_n_8_2s_21_lz_0.0.vec

where we have used the reference file

   NbrParticles=8
   LzMax=21
   ReferenceState=1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1


The unnormalized state can be converted to the cylinder geometry using FQHECylinderNormalizeState

$PATHTODIAGHAM/build/FQHE/src/Programs/FQHEOnCylinder/FQHECylinderNormalizeState -i fermions_unnormalized_haldane_n_8_2s_21_lz_0.0.vec --haldane --reference-file laughlin3_n_8_2s_21.dat --cylinder-perimeter 9.0 --normalize --output-file fermions_haldane_cylinder_perimeter_9.000000_n_8_2s_21_lz_0.0.vec

To obtain the density profile, we just have to run

$PATHTODIAGHAM/build/FQHE/src/Programs/FQHEOnCylinder/FQHECylinderDensity --nbr-points 400 --haldane --reference-file laughlin3_n_8_2s_21.dat --input-state fermions_haldane_cylinder_perimeter_9.000000_n_8_2s_21_lz_0.0.vec

The code will create a file fermions_haldane_cylinder_perimeter_9.000000_n_8_2s_21_lz_0.0.rho.dat (replacing the .vec extension with .rho.dat). This text file should look like

   # Length = 15.35889741755, Perimeter = 9, Aspect ratio = 0.58597956320198
   # 0 0 0 (0.54756193124569,0)
   # 1 0 0 (0.43662316354643,0)
   # 2 0 0 (0.40006895675818,0)
   # 3 0 0 (0.36705856641123,0)
   # 4 0 0 (0.25514337026317,0)
   # 5 0 0 (0.26513773727377,0)
   # 6 0 0 (0.41770106572259,0)
   # 7 0 0 (0.30891888141043,0)
   # 8 0 0 (0.30625304866107,0)
   # 9 0 0 (0.40465377729257,0)
   # 10 0 0 (0.29087950141488,0)
   # 11 0 0 (0.29087950141488,0)
   # 12 0 0 (0.40465377729257,0)
   # 13 0 0 (0.30625304866107,0)
   # 14 0 0 (0.30891888141043,0)
   # 15 0 0 (0.41770106572259,0)
   # 16 0 0 (0.26513773727377,0)
   # 17 0 0 (0.25514337026317,0)
   # 18 0 0 (0.36705856641123,0)
   # 19 0 0 (0.40006895675818,0)
   # 20 0 0 (0.43662316354643,0)
   # 21 0 0 (0.54756193124569,0)
   -12.679448708775 1.1580477168475e-13 1.0638527610851e-14
   -12.616209563095 2.2689176354567e-13 2.1094680462658e-14
   -12.552970417416 4.4099979670168e-13 4.1484099343606e-14
   -12.489731271736 8.5032613162762e-13 8.0937838883275e-14
   -12.426492126056 1.6265231331468e-12 1.5664760134065e-13
   ...


The commented region provides the occupation numbers in orbital space. The first column is the orbital index and the fourth is the occupation number, while the second and the third column are the left and right state index (both 0 here since we have a single state). Below the commented region is the density (integrated over the perimeter) in real space (second column) as a function of the position along the cylinder axis (first column). The third column is the integrated charge from minus infinity to the position given by the first column.