One of the main features of Pybinding is an easy-to-use and fast model builder: it constructs the tight-binding Hamiltonian matrix. This can be a demanding task for large or complicated systems (with many parameters). Great care was taken to make this process fast.
We compare the performance of Pybinding with the Kwant package. Both code packages are based on the numerical tight-binding method and can build identical Hamiltonian matrices. For calculations involving these matrices, the packages specialize in different ways: Kwant is intended for transport calculations with scattering systems while Pybinding targets large finite-sized and periodic systems in 1 to 3 dimensions. Pybinding can also be used to construct scattering systems, however it does not have a builtin solver for transport problems. This is where the Kwant compatibility layer comes in: it’s possible to build a system in Pybinding and use Kwant’s solvers for transport calculations. This combination takes advantage of the much faster model builder – see the comparison below.
The code used to obtain these results is available here:
You can download it and try it on your own computer. Usage instructions are located at the top
of the script file.
The benchmark constructs a circular graphene flake with a pn-junction and a constant magnetic field. The system build time is measured from the start of the definition to the point where the Hamiltonian matrix is fully constructed (a sparse matrix is used in both cases).
Pybinding builds the Hamiltonian much faster than Kwant: by two orders of magnitude. The main reason for this is in the way the system shape and fields are implemented. Both Kwant and Pybinding take user-defined functions as parameters for model construction. Kwant calls these functions individually for each atom and hopping which is quite slow. Pybinding stores all atoms and hoppings in contiguous arrays and then calls the user-defined functions just once for the entire dataset. This takes advantage of vectorization and drastically improves performance. Similarly, the lower memory usage is achieved by using arrays and CSR matrices rather than linked lists and trees.
Please note that at the time of writing Pybinding v0.8 does lack certain system construction features compared to Kwant. Specifically, it is currently not possible to build heterostructures in Pybinding, but this will be resolved in the near future. New features will be added while maintaining good performance.
At first glance it may seem like system build time is not really relevant because it is only done once and then multiple calculations can be applied to the constructed system. However, every time a parameter is changed (like some field strength) the Hamiltonian matrix will need to be rebuilt. Even though Kwant does take this into account and only does a partial rebuild, Pybinding is still much faster and this is very apparent in transport calculations which sweep over some model parameter. For more information and a direct comparison, see the Kwant compatibility section.