Multipoint correlation functions: spectral representation and numerical evaluation

Computing local multipoint correlators using the numerical renormalization group

“…The numerical results for checks (i) to (iv) were discussed in Ref. 1. Here, we present the underlying PSFs and the results for check (v).…”

“…We begin with a summary of the spectral representations of p correlators derived in Ref. 1, defining p PSFs and their convolution kernels. To describe key ideas and introduce notation, we will first focus on the ZF, stating analogous MF and KF results thereafter.…”

“…Due to the multiplicative structure of Eq. (1), G(ω) can be expressed as an ( −1)fold convolution of the Fourier transforms of K and the operator product, resulting in an expression of the form (3) . (4) (Note that different fonts distinguish the integer index i from the imaginary number i.)…”

“…In an accompanying paper [1], we described a novel approach for analyzing and computing -point ( p) correlators. Its central idea is to separate system-dependent spectral information from formalism-dependent analytic properties.…”

“…The local 4p vertices shown in Ref. 1 were computed using a generalization of the numerical renormalization group (NRG) [19,20]. This powerful impurity solver allows one to directly compute real-frequency correlators, at arbitrarily low temperatures, with exponentially fine resolution at the lowest excitation energies.…”