How to set the grid in kwant.continuum.discretize?
Dear Kwanters, The kwant.continuum.discretize helps transform a continuous k.p Hamiltonian to a tight-binding Hamiltonian. During this discretizing process, we can use the "grid" parameter to control the "mesh" of such a discretization. In the tutorial, I see that different "grid" result in different approximations of the tight-binding Hamiltonian with respect to the continuous Hamiltonian. See https://kwant-project.org/doc/1/tutorial/discretize My question is: which value of grid should we use during the discretizing process? Should we decrease the "grid" from a larger value to a smaller value, monitoring the band structure and conductance behavior, until the band structure and conductance behavior remain almost unchanged when further decreasing the "grid"? Thanks a lot for your answer.
dielectric_hjzhao@126.com wrote:
My question is: which value of grid should we use during the discretizing process? Should we decrease the "grid" from a larger value to a smaller value, monitoring the band structure and conductance behavior, until the band structure and conductance behavior remain almost unchanged when further decreasing the "grid"?
Hi, it is in general (independently of Kwant) a good idea to setup numeric simulations such that resolutions (there can be several, e.g. in space, time, energy) are explicit parameters that can be modified and thus controlled. Increasing a resolution will generally provide more accurate results at the cost of more time and resource usage. (But you can also hit a wall where accuracy is limited by something else.) You need to find a compromise between the accuracy you desire and the resources required. To this end, it is often useful to plot the computed quantity as a function of resolution (starting at really low resolutions) and try to assess whether and how it converges.
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dielectric_hjzhao＠126.com