FDM spectrum

The fdmSpectrum class computes spectral functions from the reduced density matrix and the kept NRG states. It is the main entry point for dynamical correlation functions in the full density matrix framework.

How the spectrum is assembled

An fdmSpectrum instance refers to an nrgcore object and accumulates contributions as its Wilson shells are visited. Before processing shells, setOperator registers a required operator set B and an optional corresponding set A. If A is omitted, the adjoint of each B block is used. The operator vectors are held by pointer, so they must remain alive while the spectrum is being calculated.

For each shell, calcSpectrum updates the kept-state indices and constructs a sector density matrix. On the final shell, weights are initialized from the shell ground-state degeneracy; on later shells, the reduced density matrix from the next shell is carried on kept states. The operator contraction evaluates the two operator-density-matrix orderings for each pair of sectors and bins their energy differences, scaled by the provided energyScale, into separate positive- and negative-frequency arrays. Small contributions below the internal weight tolerance are skipped.

After the contraction, the full density matrix is rotated into the coupled system-bath basis and traced over the bath to produce the reduced matrix used by the next shell. Once all shells have contributed, saveFinalData writes the logarithmic energy grid and the positive and negative weight arrays through the provided file object, then clears the accumulated weights. The internal grid defaults to 100,000 points over the energy range from 1e-10 to 10.

For the detailed generated API reference, see the fdmSpectrum class documentation.