Fig. 1: An example demonstrating that modifying eigenvalues can recover the localization of the Hamiltonian.
From: Hamiltonian transformation for accurate and efficient band structure interpolation
a Original tridiagonal Toeplitz Hamiltonian T for a 1-D atomic chain with nearest-neighbor interactions. b Corresponding eigenvalue spectrum of T. c Reconstructed Hamiltonian after spectral truncation, leading to delocalization. d Truncated eigenvalue spectrum with eigenvalues below 1.5. e Reconstructed Hamiltonian after shifting the remaining eigenvalues downward by 1.5, showing improved localization. f Adjusted eigenvalue spectrum after the shift, restoring continuity.
