# FQHETorusFermionsWithTranslationsGenericNBody

FQHETorusFermionsWithTranslationsGenericNBody diagonalizes any n-body interaction defined by its Fourrier transform for a fermionic system on the torus geometry. The usage is similar to FQHEFermionsTorusWithTranslation. By default, the interaction is set to be the n-body hollowcore interaction. Notice that if you are interested in this specific interaction and you want to focus on rectangular tori, you should better use FQHETorusFermionsWithTranslationsNBodyHollowCore.

If we want to look at the Moore-Read state on the torus, we just have to use

*$PATHTODIAGHAM/build/FQHE/src/Programs/FQHEOnTorus/FQHETorusFermionsWithTranslationsGenericNBody -p 4 -l 8 --nbr-nbody 3 --full-reducedbz --use-lapack*

The generated spectrum fermions_torus_3body_hollowcore_n_4_2s_8_ratio_1.000000.dat will look like

# Kx Ky E 0 0 0.29992219194192 0 0 0.46812701274052 0 1 0.20197428837541 0 1 0.54404482703396 0 2 -2.2204460492503e-16 0 2 0.3961797599951 0 2 0.79602347618827 ...

The code also store the interaction matrix elements. In this example, it creates a file 3body_hollowcore_interactioncoefficient_2s_8_ratio_1.0000000000.dat. If the file is in the current directory, any diagonalization for 3-body hollow core with 8 flux quanta will re-read this file instead of generating the interaction matrix elements. If you want to regenerate the interaction file, you can either erase it or add the --regenerate-interactionelements option. Since generating the interaction matrix elements is highly time consuming (this part of the code is full parallelized, so you should use -S with the maximum number of processors), re-reading the interaction matrix elements from the hard drive spares a lot of time.

By default, the code uses a rectangular torus. This can be changed by setting the --angle option to a non-zero value. This latest option allows to set the angle (in pi units, contrary to FQHEFermionsTorusWithTranslation) between the two vectors 1 and <math>\tau</math> that span the torus. All output file names will contain the angle in radian units. Notice that the length of <math>\tau</math> (or more precisely the ratio of lengths between <math>\tau</math> and 1 is set via the --ratio option.