Hi Jannis,
You mentioned that you system is infinite and has translational symmetry, yet you are using 'hamiltonian_submatrix'. 'hamiltonian_submatrix' probably does not return what you want; what should it return when the system is infinite, as it is in your case? Probably you want to construct the k-space Hamiltonian and work with that. You could do that with the following function: def H_k(k, params): H_0 = syst.cell_hamiltonian(params=params) V = np.zeros_like(H_0) V += syst.inter_cell_hopping(params=params) return H_0 + V * exp(1j * k) + V.conjugate().transpose() * exp(-1j * k) If you are just interested in the eigenvalues/vectors you can also use 'kwant.physics.Bands', which will allow you to evaluate the eigenvalues/vectors given a k (check out the documentation to find out how to get the eigenvectors in addition to the eigenvalues). I would first rectify this before looking any further. Happy Kwanting, Joe > I am trying to calculate the total energy of the electrons in an > s-wave superconducting lead with spins. But I am not sure, if my > method is correct. > > Currently I separate the particle and hole Hamiltonians with a projector > > H = syst.hamiltonian_submatrix(params=params) > P_electron = np.kron(np.eye(L+1), np.array([[1, 0, 0, 0], [0, 1, > 0, 0], [0, 0,0,0], [0, 0,0,0]])) > H_electron = P_electron.conjugate().transpose() @ H @ P_electron > > where L is the number of sites. L+1 because I get a dimension mismatch > otherwise. My guess here is, that kwant generates an extra site > because of the translational symmetry. For the conservation laws I used > > particle_hole=pauli.sxs0, conservation_law=-pauli.szs0 > > where pauli.sisj is the kroneker product of the i-th and the j-th > pauli matrix. For my Hamiltonian I used the base (e_up, e_down, > h_down, h_up). > > Then I calculate the eigenvalues of H_electron and multiply them with > the fermi distribution to get the total energy. > > spectrum= np.linalg.eigvalsh(H_electron) > fermi_dist=kwant.kpm.fermi_distribution(spectrum, params["mu"], T) > total_energy=np.dot(fermi_dist,spectrum) > > Now to the part, why I suspect a mistake in my method. I use a > spin-dependent hopping term and scan over a parameter /b/, that > changes the spin dependency. When doing so the qualitative behavior of > the total energy /E_total(b)/ changes with the size of my unit cell. > But all sites in my unit cell are identical. So I would suspect, that > the results should only differ by a factor. For large systems the > curvature of /E_total(b)/ converges, but for small systems the results > vary quit a lot. > > I'd really appreciate some help on this. > Best regards, > Jannis >
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