Use exact diagonalization to study the Josephson effect in case of lead order parameter
Usage:
There are many ways to install the required QuSpin package. The standard way is to make an Anaconda environment by e.g.
conda create --name josephsonED
conda install -n josephsonED matplotlib
conda install -n josephsonED -c weinbe58 omp quspin
The environment can be then activated or deactivated by
conda active josephsonED
conda deactivate
Then you can run the codes by
python3 example_name.py
There are two versions of the code:
-
Josephson_ED_varied_number.py
considers the system in two independent blocks: the even particle (up spin + down spin particles) number and the odd particle number. This version gives sensible results. Now it considers sawtooth lattice but one can also build other models -
Josephson_ED_constant_ph.py
considers the system in many independent branches: on each the up spin particle number + down spin hole number is constant (conserved quantity within the considered Hamiltonian).