Dear Kwant Developers, I understand that a symmetry operator (the conservation law) can be used to block diagonalize the lead hamiltonian, as in the separation of the electrons and holes in superconductors. In the electronhole case, the symmetry operator is [[1,0],[0,1]]. There are two eigenvalues (+1, 1) and the eigenvalues are different. Can the kwant code be used to handle a symmetry operator like [[0,0,0,0],[0,0,0,0],[0,0,1,0],[0,0,0,1]]. There are four eigenvalues in two degenerate pairs. This is like a system with four orbitals in a unit cell and each pair of orbitals have the same energy. There are two possible scenario. With this symmetry operator, the lead Hamiltonian is block diagonalized into two blocks. Can the conservation law function handle this case? What would happen if the hopping can split the degenerate eigenvalues within a single block? Can the conservation law function handle this case too? KS Chan Disclaimer: This email (including any attachments) is for the use of the intended recipient only and may contain confidential information and/or copyright material. If you are not the intended recipient, please notify the sender immediately and delete this email and all copies from your system. Any unauthorized use, disclosure, reproduction, copying, distribution, or other form of unauthorized dissemination of the contents is expressly prohibited.
Dear KS Chan The conservation law feature can handle degenerate eigenvalues. The number of blocks is equal to the number of distinct eigenvalues of the conservation law, and the degeneracy of each eigenvalue gives the size of the block. So in your example, the Hamiltonian will indeed be block diagonalized into two blocks that are 2x2 each, corresponding to the eigenvalues 0 and 1, respectively. Note that a valid conservation law must block diagonalize the lead Hamiltonian, which means that the conservation law must simultaneously block diagonalize both the hopping matrix and the onsite matrix, and so the hopping cannot split the degeneracies of a valid conservation law. If one tries to declare a conservation law that does not block diagonalize both the hopping and the onsite matrix, Kwant should raise an error. Best, Tómas On Tue, Jun 19, 2018 at 8:48 PM, Prof. CHAN Kwok Sum <apkschan@cityu.edu.hk> wrote:
Dear Kwant Developers,
I understand that a symmetry operator (the conservation law) can be used to block diagonalize the lead hamiltonian, as in the separation of the electrons and holes in superconductors. In the electronhole case, the symmetry operator is [[1,0],[0,1]]. There are two eigenvalues (+1, 1) and the eigenvalues are different. Can the kwant code be used to handle a symmetry operator like [[0,0,0,0],[0,0,0,0],[0,0,1,0],[0,0,0,1]]. There are four eigenvalues in two degenerate pairs. This is like a system with four orbitals in a unit cell and each pair of orbitals have the same energy. There are two possible scenario. With this symmetry operator, the lead Hamiltonian is block diagonalized into two blocks. Can the conservation law function handle this case? What would happen if the hopping can split the degenerate eigenvalues within a single block? Can the conservation law function handle this case too?
KS Chan
Disclaimer: This email (including any attachments) is for the use of the intended recipient only and may contain confidential information and/or copyright material. If you are not the intended recipient, please notify the sender immediately and delete this email and all copies from your system. Any unauthorized use, disclosure, reproduction, copying, distribution, or other form of unauthorized dissemination of the contents is expressly prohibited.
participants (2)

Prof. CHAN Kwok Sum

Tómas Örn Rosdahl