dmft/hybridization: apply the MC sign once in measure_Gl

[skilledwolf]

Problem

hybmatrix::measure_Gl multiplies the Monte Carlo configuration sign into both factors of every contribution: once into M_ji and once into bubble_sign:

double M_ji = operator() (j, i) * sign;
...
double bubble_sign = sign;            // (flipped on tau wraparound)
...
double gl = M_ji*legendre_p*bubble_sign;   // carries sign^2 = 1

Each accumulated term therefore carries sign² = 1, so the Legendre estimators Gl/Fl ignore the configuration sign entirely — while measure_G (binned τ) and measure_Gw (Matsubara) apply it exactly once via bubble_sign. In any run with ⟨sign⟩ ≠ 1 the Legendre channel accumulates the unweighted average while the other channels accumulate the sign-weighted numerator: the channels are mutually inconsistent and Gl/Fl are biased.

Fix

One line: drop the sign from M_ji, so it enters exactly once through bubble_sign, matching measure_G/measure_Gw. The τ-wraparound anticommutator flip on bubble_sign is unchanged.

Sign-free runs (the common density-density segment case, where sign = 1 throughout) are bit-identical — which is how this survived; MEASURE_legendre also defaults off.

How to verify

There is deliberately no runtime reproducer in this PR: exercising the bug end-to-end needs a model with ⟨sign⟩ ≠ 1 and MEASURE_legendre=1, and there is no signful reference result in-tree to compare against. The bug is instead verifiable by inspection in under a minute at the quoted lines of measure_Gl: M_ji carries sign, bubble_sign carries sign again, and every accumulated term is M_ji * legendre_p * bubble_sign — so the configuration sign enters squared and cancels identically, while measure_G/measure_Gw in the same file apply it exactly once via bubble_sign. Equivalently: flip the sign of sign at the call site and observe that Gl/Fl are unchanged while G/Gw negate.

The downstream fork pins the fix with a sign-linearity test: a deterministic two-operator-pair hybridization matrix built through the production insert path must satisfy measure(sign=−1) == −measure(sign=+1) elementwise for all of G/F/Gl/Fl. Before the change Gl/Fl return identical values for both signs (G/F already pass); after it all four channels are exactly sign-antisymmetric. (That test rig depends on fork-side scaffolding and is not ported here; happy to port it if wanted.) The solver builds cleanly with the change on current master (73b331006).

Provenance

Found in a systematic estimator audit in a downstream ALPS modernization fork; the fix is identical there and covered by the sign-linearity lock described above.

[egull]

Looks good. Likely hard to test in a 'real world' scenario since the typical cases we use for this code are sign-free.