Accurate Study from Adaptive Perturbation Method

TL;DR

This paper introduces an adaptive perturbation method for Hamiltonian decomposition, enabling precise spectral and expectation value calculations for complex quantum systems, including applications to particle physics models.

Contribution

The paper presents a novel adaptive perturbation approach that yields exact solutions for perturbed terms, improving accuracy in quantum spectral analysis and extending to Higgs field models.

Findings

Accurate spectrum and $ angle x^2 angle$ calculations up to next-leading order

Exact solutions for each perturbed term

Application to Higgs field model demonstrating versatility

Abstract

The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and non-diagonal elements of the Fock state. The diagonal elements of the Fock state are solvable but can contain the information about coupling constants. We study the harmonic oscillator with the interacting potential, $\lambda_1x^4/6+\lambda_2x^6/120$, where $\lambda_1$ and $\lambda_2$ are coupling constants, and $x$ is the position operator. In this study, each perturbed term has an exact solution. We demonstrate the accurate study of the spectrum and $\langle x^2\rangle$ up to the next leading-order correction. In particular, we study a similar problem of Higgs field from the inverted mass term to demonstrate the possible non-trivial application of particle physics.