Optimization of perturbative similarity renormalization group for Hamiltonians with asymptotic freedom and bound states

TL;DR

This paper demonstrates how tuning the similarity renormalization group procedure enhances the convergence and accuracy of perturbative calculations for Hamiltonians with asymptotic freedom and bound states, achieving a few-percent precision.

Contribution

It introduces a method to optimize the generator of the similarity transformation, improving perturbative effective Hamiltonian calculations for complex quantum systems.

Findings

Enhanced convergence of perturbative calculations.

Achieved a few-percent accuracy in bound state energy estimation.

Validated approach using a model Hamiltonian with asymptotic freedom.

Abstract

A model Hamiltonian that exhibits asymptotic freedom and a bound state, is used to show on example that similarity renormalization group procedure can be tuned to improve convergence of perturbative derivation of effective Hamiltonians, through adjustment of the generator of the similarity transformation. The improvement is measured by comparing the eigenvalues of perturbatively calculated renormalized Hamiltonians that couple only a relatively small number of effective basis states, with the exact bound state energy in the model. The improved perturbative calculus leads to a few-percent accuracy in a systematic expansion.