Renormalization Treatment of IR and UV Cutoffs in Waveguide QED and Implications to Numerical Model Simulation

TL;DR

This paper derives non-perturbative renormalization relations for waveguide-QED models, explicitly addressing IR and UV cutoffs to improve the accuracy and efficiency of numerical simulations.

Contribution

It provides a first-principles derivation of renormalization relations that connect bare parameters to physical observables in waveguide-QED models, enhancing simulation reliability.

Findings

Explicit expressions linking bare parameters to physical observables

Verification of relations with scattering theory

Framework for efficient multi-photon simulations

Abstract

We present a non-perturbative, first-principles derivation of renormalization relations for waveguide-QED models, explicitly accounting for the infrared (IR) and ultraviolet (UV) cutoffs that are necessarily introduced in numerical simulations. By formulating the atomic dynamics in the time domain, we obtain explicit expressions linking the bare model parameters to the physically observable atomic frequency and decay rate, and verify their consistency with scattering theory. We further connect these results to standard Feynman diagrams, providing a transparent physical interpretation and ensuring the generality of the approach. Finally, we show how these renormalization relations can be used to parameterize simulations with a minimal frequency bandwidth, simultaneously preserving physical accuracy and reducing computational cost, thereby paving the way for efficient and reliable multi-photon light-matter simulations.