How does the grid spacing in kwant.continuum.discretize effect the system?
Dear Kwant developers, I am currently simulating a carbon nanotube system by defining a 1D scattering region as: def kwant_shape(site): (z,) = pos return (-total_length / 2 <= z < total_length/ 2) I then build the system by discretizing a continuous Hamiltonian onto the grid region, as shown in the function below: def make_system(): lattice_size = total_length / number_of_lattices template = kwant.continuum.discretize(hamiltonian, grid=lattice_size) syst = kwant.Builder() # add the nanotube to the system syst.fill(template, kwant_shape, (0,)) syst = syst.finalized() return syst The lowest eigenvector of the Hamiltonian system is calculated and evolved over time using Tkwant. However, by changing the parameter 'number_of_lattices', hence using a different size grid spacing, the response of the system is very different. Sometimes the resulting graph shows a changing density of the wavefunction (which is expected), however for certain lattice points there is no change in the graph, suggesting that the system does not evolve. For example, for 40 lattice points I get the expected response however for 60 lattice points I do not. I was wondering why changing the grid spacing might affect the response of the state being evolved by Tkwant? Could it be due to the symmetry of the system or how the system is defined? Thank you for any help with this!
Hi Isobel, As you decrease the discretization grid spacing you should approach the continuum limit. For example, the band structure should become more and more accurate also for larger momenta. Did you check the Kwant tutorial on the discretizer? In particular the example comparing a=1.0 and a=0.25: https://kwant-project.org/doc/1/tutorial/discretize#limitations-of-discretiz... Tkwant should not really matter here. I suggest that you first check whether your discretization behaves as it should without even using tkwant, for example by looking at the band structure. Cheers Christoph
participants (2)
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Christoph Groth
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Clarke, Isobel