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FQHESphereFermionsWithSpin provides exact diagonalization of any two-body hamiltonian for fermions with SU(2) on the sphere geometry. The way to use this code close to the one of FQHESphereFermionsTwoBodyGeneric. FQHESphereFermionsWithSpin works in a given sector of total spin projection along z (Sz) that can be set using the -s or --total-sz option. The code also supports the option to work in the space containing all possible Sz components, this can be activated with the option --all-sz.

The interaction is specified through its Haldane pseudo-potentials. Such a file can be generated using CoulombPseudopotentials for SU(2) invariant interaction. In the most generic case, it looks like

   PseudopotentialsUpUp = 1.0 1.0 1.0 0.0 0.0 0.0
   PseudopotentialsDownDown = 1.0 1.0 1.0 0.0 0.0 0.0
   PseudopotentialsUpDown = 1.0 0.0 0.0 0.0 0.0 0.0

This example, for the Halperin (331) state, shows the naming convention to provide the pseudo-potentials between two spin up, two spin down and spin up / spin down.

Additionally, it is possible to specify different combinations of one-body potentials, using "OneBodyPotentialUpUp", "OneBodyPotentialDownDown" (useful for adding a Zeeman term), while the Sx term can be defined using "OneBodyPotentialUpDown" (this is also useful for implementing tunnelling term in a bilayer simulation).