# FQHETorusBosonsWithSU4SpinTwoBodyGeneric

FQHETorusBosonsWithSU4SpinTwoBodyGeneric is the analogue of FQHETorusBosonsWithSU3SpinTwoBodyGeneric for bosons having a SU(4) internal degree of freedom on the torus geometry. Only the translation along the y direction is taken into account. Many options are thus similar to the ones of FQHETorusBosonsWithSU3SpinTwoBodyGeneric. The SU(4) sectors are defined by the three quantum numbers $S_z$ (spin), $I_z$ (isospin) and $P_z$, they are related to the number of particles per component $N_1, N_2, N_3$ and $N_4$ through the relation

$S_z=\frac{N_1+N_2-N_3-N_4}{2}$, $I_z=\frac{N_1+N_3 -N_2-N_4}{2}$ and $P_z=\frac{N_1+N_4 -N_2-N_3}{2}$

The SU(4) sector can be set through the --total-sz (for $S_z$), --total-isosz (for $I_z$) and --total-entanglement options (for $P_z$) or through --nbr-n1, --nbr-n2, --nbr-n3, --nbr-n4 (for $N_1, N_2, N_3$ and $N_4$ ). Unless the sum of the values given by --nbr-n1, --nbr-n2, --nbr-n3, -nbr-n4 matches the total number of particles, --total-sz, --total-isosz and --total-entanglement are used by default.

The interaction file that describes the two body interaction is similar to the one used for FQHESphereFermionsWithSpin or FQHETorusBosonsWithSU3SpinTwoBodyGeneric. Interactions between each species are defined by ten pseudo-potentials :

• PseudopotentialsUpPlusUpPlus
• PseudopotentialsUpPlusUpMinus
• PseudopotentialsUpPlusDownPlus
• PseudopotentialsUpPlusDownMinus
• PseudopotentialsUpMinusUpMinus
• PseudopotentialsUpMinusDownPlus
• PseudopotentialsUpMinusDownMinus
• PseudopotentialsDownPlusDownPlus
• PseudopotentialsDownPlusDownMinus
• PseudopotentialsDownMinusDownMinus

Here UpPlus stands for the type 1 particles, UpMinus stands for the type 2 particles, DownPlus stands for the type 3 particles and DownMinus stands for the type 4 particles. If an additional generic Pseudopotentials is provided, it will replace any missing pseudo-potential term. Note that the number of pseudo-potentials per interaction does not need not match the number of flux quanta. For example, the following file

   Pseudopotentials = 1.0


is enough to define the interaction that produces the exact interaction related to the generalized Halperin state [2,1], irrespective to the number of particles or flux quanta.