FQHEDiskFermionsTwoBodyGeneric

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FQHEDiskFermionsTwoBodyGeneric provides exact diagonalization for fermions on a disk geometry and any generic two body interaction described by its pseudo-potentials. Its usage has many similarities with FQHESphereFermionsTwoBodyGeneric.

Simple usage

By default the fermionic Hilbert space is only constraint by the number of particles and the system total angular momentum. The range of this latest can be set by the two options --maximum-momentum ( or -l) and --minimum-momentum. Unless specified, this latest is automatically set to the lowest possible one for the current number of particles.

Let's consider the <math>V_1</math> pseudopotential and a system with 5 electrons. We just have to run

$PATHTODIAGHAM/build/FQHE/src/Programs/FQHEOnDisk/FQHEDiskFermionsTwoBodyGeneric -p 5 --interaction-file pseudopotentials_v1.dat --interaction-name v1 --maximum-momentum 32 --use-lapack

where the pseudo-potential file pseudopotentials_v1.dat is

 Pseudopotentials = 0.0 1.0

Note that only the pseudo-potentials from the 0 to the last non-zero one have to be provided. The energy spectrum is stored in fermions_disk_v1_n_5_lz_32.dat and should look like

   # Lz E
   10 1.6164173907771
   11 1.6164173907771
   12 1.5293795312737
   12 1.6164173907771
   ...
   29 1.4503079006973
   29 1.5293795312737
   29 1.6164173907771
   30 -3.441691376338e-15
   30 0.13343225774049
   30 0.13670167629347
   30 0.13977592234891
   ...

The first zero energy state occurs at total angular momentum <math>L_z=3N(N-1)/2=30</math> as expected for the Laughlin 1/3 state.

The number of orbitals can also be truncated by using the --force-maxmomentum option if it is set to a zero or positive (by default, it is set to -1).