  First-principles electronic band structure calculations are essential for
understanding periodic systems in condensed matter physics and materials
science. We propose an accurate and parameter-free method, called Hamiltonian
transformation (HT), to calculate band structures in both density functional
theory (DFT) and post-DFT calculations with plane-wave basis sets. The cost of
HT is independent of the choice of the density functional and scales as
$\mathcal{O}(N_e^3N_k\log N_k)$, where $N_e$ and $N_k$ are the number of
electrons and the number of $\mathbf{k}$-points. Compared to the widely used
Wannier interpolation (WI), HT adopts an eigenvalue transformation to construct
a spatial localized representation of the spectrally truncated Hamiltonian. HT
also uses a non-iterative algorithm to change the basis sets to circumvent the
construction of the maximally localized Wannier functions. As a result, HT can
significantly outperform WI in terms of the accuracy of the band structure
calculation. We also find that the eigenvalue transformation can be of
independent interest, and can be used to improve the accuracy of the WI for
systems with entangled bands.
