Green’s function utilities

Helpers for detecting and enforcing (symmetrizing) the block structure of Green’s functions. Typically used to symmetrize impurity-solver output before feeding it into the next DMFT iteration.

Analyzing degenerate blocks

analyze_degenerate_blocks scans the matrix-valued blocks of a block Green’s function and partitions them into degenerate groups — sets of blocks that are numerically equal (up to a user-set threshold) when compared at \(\tau = 0\) or \(i\omega_0\). This decomposes the Green’s function into smaller, independent blocks so that the TRIQS impurity solver can treat each unique block on its own rather than carrying redundant copies through the calculation.

Symmetrizing a block Green’s function

Given a partition \(\{ \mathcal{D}_g \}\) of degenerate blocks returned by analyze_degenerate_blocks, symmetrize replaces every block in a group by the average over the group:

\[\bar{G}_{b}(\omega) = \frac{1}{|\mathcal{D}_g|} \sum_{b' \in \mathcal{D}_g} G_{b'}(\omega), \qquad G_{b}(\omega) \;\leftarrow\; \bar{G}_{b}(\omega) \quad \forall\, b \in \mathcal{D}_g.\]

This enforces the degeneracy exactly, removing any residual numerical breaking introduced by the impurity solver.

triqs_modest.utils.analyze_gfs.analyze_degenerate_blocks	Find the generate blocks of a block GF by analyzing \(G(\tau=0)\) or \(G(i\omega_0)\) using the
triqs_modest.utils.analyze_gfs.symmetrize	Symmetrize the blocks of a block Green's function given a list of it's degenerate blocks.