# FQHETorusFermionsWithSpinTwoBodyGeneric

FQHETorusFermionsWithSpinTwoBodyGeneric allows to consider fermions with a SU(2) degree of freedom on the torus geometry. Only the translation along the y direction is taken into account. Many options are similar to the ones of QHEFermionsTwoBodyGeneric or FQHESphereFermionsWithSpin. The aspect ratio of the torus is by default set to 1 and can be tuned using --ratio optio. The two vectors that define the torus are orthogonal. Unless the --redundant-kymomenta option is set, the program only computes the spectrum in momentum sector not related by the center of mass symmetry.

Similar to FQHESphereFermionsWithSpin, a file describing the interaction should be provided. Contrary to FQHESphereFermionsWithSpin, the number of pseudo-potentials does not have to match the number of flux quanta. For example, the following file pseudopotentials_torus_331.dat

PseudopotentialsUpUp = 0 1 PseudopotentialsDownDown = 0 1 PseudopotentialsUpDown = 1

is a perfectly valid file to describe the model interaction that gives rise to the Halperin (331) state.

A typical usage of FQHETorusFermionsWithSpinTwoBodyGeneric is

*$PATHTODIAGHAM/build/FQHE/src/Programs/FQHEOnTorus/FQHETorusFermionsWithSpinTwoBodyGeneric -p 4 -l 8 --interaction-file pseudopotentials_torus_331.dat --interaction-name 331 --use-lapack*

This will generate the spectrum for the model interaction described in pseudopotentials_torus_331.dat for 4 fermions at filling factor nu=1/2 .