Dynamical Spectral Function From Numerical Renormalization Group: A Full Excitation Approach

TL;DR

This paper introduces a full excitation approach to compute dynamical spectral functions from the numerical renormalization group, capturing all excitations and avoiding causality issues present in previous methods.

Contribution

It provides exact expressions for dynamical quantities in NRG and demonstrates a full excitation method that improves spectral function calculations.

Findings

The method captures intra- and inter-shell excitations.

It guarantees the sum rule for spectral functions.

It avoids causality problems of the FDM method.

Abstract

For a given quantum impurity model, Wilson's numerical renormalization group (NRG) naturally defines a NRG Hamiltonian whose exact eigenstates and eigenenergies are obtainable. We give exact expressions for the free energy, static, as well as dynamical quantities of the NRG Hamiltonian. The dynamical spectral function from this approach contains full excitations including intra- and inter-shell excitations. For the spin-boson model, we compare the spectral function obtained from the present method and the full density matrix (FDM) method, showing that while both guarantee rigorous sum rule, the full excitation approach avoids the causality problem of FDM method.