FCIHofstadterModel

FCIHofstadterModel deals with interacting particles on the Hofstadter model. It provides support for both bosons and fermions, spinless or spinful, with or without Gutzwiller projection (i.e. hardcore particles).

Basic usage

As a warm-up, we start with the Hofstadter model on a square lattice. For simplicity, we focus on hardcore bosons. A typical usage is

$PATHTODIAGHAM//build/FTI/src/Programs/FCI/FCIHofstadterModel --real-space -p 2 -x 4 -y 2 -X 1 -Y 3 --use-lapack --hardcore --boson -q 1 --full-diag 5000

Here we use two hardcore bosons having set the option --boson, --hardcore and -p 2. The lattice itself is defined through the following parameters :

• -x 4 is the number of magnetic unit cell along the x direction (here 4)
• -y 2 is the number of magnetic unit cell along the y direction (here 2)
• -X 3 is the number of sites along the x direction within the magnetic unit cell
• -Y 1 is the number of sites along the y direction within the magnetic unit cell

This means that the physical lattice has 3 * 4 * 2 = 24 sites, 12 along the x direction and 2 along the y direction. Unless explicitly specified through the -q option, the number of flux quanta through one magnetic unit cell is set to one. The flux density is equal to q / (X * Y). Note that the code is only working if -Y is set to one, another choice might lead to erroneous results.

If the hardcore constraint is removed, we can freely set the strength of the on-site density-density interaction using the --u-potential option.