Table 1 Theoretical time complexity of various procedures in Hamiltonian transformation
From: Hamiltonian transformation for accurate and efficient band structure interpolation
Operation | Algorithm | Time complexity |
Construct basis set | Randomized QRCP | \({\mathcal{O}}({N}_{\mu }^{2}({N}_{r}+{N}_{b}{N}_{k}))\) |
Construct Hamiltonian | Matrix multiplication | \({\mathcal{O}}({N}_{\mu }^{2}{N}_{b}{N}_{k})\) |
Fourier interpolation | Fast Fourier transform (FFT) | \({\mathcal{O}}({N}_{\mu }^{2}{N}_{k}\log ({N}_{k}))\) |
Nonuniform FFT (NUFFT) or butterfly factorization37 | \({\mathcal{O}}({N}_{\mu }^{2}{N}_{q}\log ({N}_{q}))\) | |
Diagonalization | Iterative diagonalization | \({\mathcal{O}}({N}_{\mu }^{2}{N}_{b}{N}_{q})\) |
