I want to calculate the winding number of the non-Hermitian Hamiltonian, without any similarity transformation. Is there any way to do that numerically without knowing the functional form of thita?
See Eqs. (5) and (6) in PHYSICAL REVIEW X 8, 031079 (2018) and Eq. (41) in PHYSICAL REVIEW X 9, 041015 (2019).
Thank you Dipendu,
Actually, I want to calculate the winding number numerically. What I mean is,
If I have a Hamiltonian, I will do diagonalization and get E and vectors, from there, could we calculate the winding number numerically, which out prior knowlegede of analytical methods ?
Yes, you can do that using any numerical language. First, you just put the expression of the eigenvalues and eigenvectors into the equations and differentiate, followed by integration over the Brillouin zone.
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