Difference between revisions of "FQHE programs"

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* [[FQHESphereCP2GenericInteraction]] :
* [[FQHESphereCP2GenericInteraction]] :
==Basic usage==
[[FQHESphereCP2GenericInteraction]] allows one to diagonalize any two-body interaction in the lowest Landau level of the CP2 geometry. The generic use is:
''$PATHTODIAGHAM/build/FQHE/src/Programs/FQHEOnSphere/FQHESphereCP2GenericInteraction -p 2 -l 3 --interaction-name V1 --interaction-file pseudopotential_v1.dat --use-lapack''
The form of the interaction is defined in an ASCII file provided in the --interaction-file option. It specifies the value of all two-body pseudopotentials. It should contain one line of the form:
    Pseudopotentials = 0 1
One also has to provide the list of all Clebsch-Gordan coefficients necessary for the composition of SU(3) momenta. A particle in the lowest Landau level of the CP2 geometry is in a (N_{\phi},0) SU(3) representation, where
(p,0) \otimes (p,0) = \oplus_{p' = 0}^{p} \left( 2(p - p'), p' \right)
This will diagonalize the coulomb interaction in each Lz sectors. Option -p sets the number of particles and -l the one-body maximum angular momentum (which matches the number of flux quanta in the lowest Landau level). Running this command produces one file named fermions_cp2_V1_n_2_2s_3.dat that looks like :
    # tz y E
    1 -9 1
    0 -6 1
    0 -6 1
    2 -6 1
    1 -3 2.2204460492503e-16
    1 -3 1
    1 -3 1
    0 0 -6.1309083055668e-31
    0 0 1
    0 0 1
    3 -3 1.1102230246252e-16
    3 -3 1
    ...
This a three-column ASCII file. The first column is the tz sector (rounded to the closest lower integer), the second column is the y sector and the third column is the energies sorted from the lowest to the highest. The name of the interaction appearing in the output file is set using the --interaction-name option.
* [[FQHESphereCP2BosonsDelta]] :
* [[FQHESphereCP2BosonsDelta]] :



Revision as of 09:09, 6 October 2015

These are all the available programs in DiagHam that are related to the Fractional Quantum Hall Effect

Sphere geometry

Jack polynomials

Entanglement spectra

Exact diagonalization

Tools

Torus geometry

Exact diagonalization

Tools

Entanglement spectra


CP2 geometry

Exact diagonalization

Basic usage

FQHESphereCP2GenericInteraction allows one to diagonalize any two-body interaction in the lowest Landau level of the CP2 geometry. The generic use is:


$PATHTODIAGHAM/build/FQHE/src/Programs/FQHEOnSphere/FQHESphereCP2GenericInteraction -p 2 -l 3 --interaction-name V1 --interaction-file pseudopotential_v1.dat --use-lapack

The form of the interaction is defined in an ASCII file provided in the --interaction-file option. It specifies the value of all two-body pseudopotentials. It should contain one line of the form:

   Pseudopotentials = 0 1 

One also has to provide the list of all Clebsch-Gordan coefficients necessary for the composition of SU(3) momenta. A particle in the lowest Landau level of the CP2 geometry is in a (N_{\phi},0) SU(3) representation, where (p,0) \otimes (p,0) = \oplus_{p' = 0}^{p} \left( 2(p - p'), p' \right)

This will diagonalize the coulomb interaction in each Lz sectors. Option -p sets the number of particles and -l the one-body maximum angular momentum (which matches the number of flux quanta in the lowest Landau level). Running this command produces one file named fermions_cp2_V1_n_2_2s_3.dat that looks like :

   # tz y E
   1 -9 1
   0 -6 1
   0 -6 1
   2 -6 1
   1 -3 2.2204460492503e-16
   1 -3 1
   1 -3 1
   0 0 -6.1309083055668e-31
   0 0 1
   0 0 1
   3 -3 1.1102230246252e-16
   3 -3 1
   ...

This a three-column ASCII file. The first column is the tz sector (rounded to the closest lower integer), the second column is the y sector and the third column is the energies sorted from the lowest to the highest. The name of the interaction appearing in the output file is set using the --interaction-name option.


Entanglement spectra

Tools

MPS