johanjoensson / rspt2spectra / 35778083680

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github

Committed by johanjoensson

Commit Message

Constrain hybridization fits to the symmetries of the data

The star-bath fit is stochastic, so any symmetry Delta(w) happens to have was
only reproduced to within the fit residual. Detect them per block and impose
them exactly.

Three families, all real-linear conditions on the Hermitian residues: orbital
degeneracy (residues confined to the *-algebra generated by the data),
antiunitary symmetry (reality and time reversal / Kramers), and particle-hole
(mirrored poles with A_{-e} = A_{+e}^T and C = -C^T).

Writing A_b = sum_p a_bp S_p with real a and an orthonormal Hermitian basis,
Tr(S_p S_q) = delta_pq is real, so the constrained normal equations decouple
across p: every coefficient column solves the same real (n_b+1)x(n_b+1) system.
That is the exact constrained optimum -- projecting the unconstrained solve is
not equivalent, since the Gram matrix is complex off-diagonal while the
coefficients are real -- and it is cheaper than the old lstsq whenever there is
symmetry to exploit. Particle-hole splits the basis by transpose parity into
two such systems.

Enforcement is on by default; --no-enforce-symmetry and --symmetry-tol control
it, and -v reports what was detected per block with its measured residual.
Particle-hole is only enforced when the fit window reaches above the Fermi
level, since mirroring puts half the poles at +e.

Two bugs fixed along the way.

hyb_fit's realvalue_v tested Hermiticity, not realness. Every physical
hybridization is Hermitian, so it was always true and A = A.real was forced
unconditionally, wrongly truncating complex residues on spin-orbit blocks. The
antiunitary family subsumes it correctly.

Inter-block particle-hole detection compared blocks at the same frequency index
rather than mirrored ones. Kramers-Kronig makes that unsatisfiable, so the
relation was never detected and build_full_bath's particle-hole branch was dead
code. Detection, build_greens_function, build_matrix, build_full_bath and
assemble_h0's constant ... (continued)

Coverage Stats

631 of 697 new or added lines in 7 files covered. (90.53%)

4 existing lines in 1 file now uncovered.

2442 of 2988 relevant lines covered (81.73%)

3.27 hits per line