Theory¶

This section details the theoretical foundations behind qkrylov. These pages provide mathematical background and explain the algorithms used under the hood.

• Exact Diagonalization: Discusses what ED is, the exponential scaling of Hilbert spaces, and its limits.
• Krylov Subspace Methods: Explains the Lanczos and Davidson algorithms for finding extremal eigenvalues in sparse systems.
• Matrix-Free Methods: Why no matrix is explicitly stored in memory, relying instead on fast action of the Hamiltonian.
• Spectral Functions: Details the continued fraction expansion approach for dynamical responses.
• Finite Temperature Lanczos Method (FTLM): Describes how thermal averages are approximated using Krylov subspaces.

Note: Most of these pages are currently under construction.