Dear Monika, Your statement is basically correct. There are several ways to obtain a tight-binding model and discretizing a continuous equation with finite difference is only one of them. Another one (actually the original way) is to start from localized orbitals and calulate the Hamiltonian in this basis (This is standard for e.g. graphene: 1 site = 1 atom). Hence, even when used outside of the scope in which they have been derived these TB models always remain "physical". For the case of the tutorial that you mention, the dispersion relation of a 1d tight-binding model is E = -2 cos (k) which indeed becomes different from the continuous spectrum E = k^2 when E is of the order unity. In practice the difference starts to be of a few percent for E ~ 1 so this condition is not too stringent. Try doing several calculations at fixed k.a (i.e. decreasing the energy as you increase the number of sites in the simulation) to get a feeling of how the continuous limit is reached.
Best, Xavier ________________________________________ De : qcon...@hotmail.com [qcon...@hotmail.com] Envoyé : lundi 8 juin 2020 09:54 À : kwant-discuss@python.org Objet : [Kwant] Accuracy of tight binding approximation in Kwant scattering problem The tight binding approximation is good for states with a wavelength considerably larger than than the lattice constant (a); equivalently (k*a<<1), where k is the wave number . In the tutorial "2.2.2. Transport through a quantum wire" of Kwant <https://kwant-project.org/doc/1.0/tutorial/tutorial1#transport-through-a-quantum-wire>, the energies, at which the conductance has been calculated, varies from 0 to 1 in units of t, where t=ћ^2/(2ma^2). Is it consistent with the validity of tight binding approximation, as it seems that would required the energy to be << 1 (in units of t)? Regards, Monika
