The Renormalized Yukawa Hamiltonian: Spectrum, Parton Distribution Functions, and Resource Estimates for Quantum Simulation

TL;DR

This paper applies the RGPEP to the Yukawa Hamiltonian to obtain a finite, renormalized effective Hamiltonian, analyzes its spectrum and parton distributions, and estimates quantum simulation resources, showing comparable costs to the bare Hamiltonian.

Contribution

It introduces a second-order renormalized Yukawa Hamiltonian using RGPEP and provides resource estimates for quantum simulation of this effective model.

Findings

Renormalized Hamiltonian is finite due to counterterms.

Spectrum and parton distribution functions are computed.

Quantum resource costs are comparable to the bare Hamiltonian.

Abstract

We apply the Renormalization Group Procedure for Effective Particles (RGPEP) to the front form Yukawa Hamiltonian, yielding a renormalized (effective) Hamiltonian, accurate up to second order in the coupling strength. Subsequently, we examine the spectrum and parton distribution functions produced by the renormalized Hamiltonian, and show that the addition of counterterms leads to finite results. Resource estimates for quantum simulation are calculated for a single `Ladder Operator Block Encoding' (LOBE), and show that the cost to block encode the renormalized Hamiltonian is comparable to block encoding the bare Hamiltonian.