High--order connected moments expansion for the Rabi Hamiltonian

TL;DR

This paper investigates the convergence of the connected moments expansion (CMX) for the Rabi Hamiltonian, revealing that the CMX often exhibits oscillations and is unreliable in practical applications.

Contribution

It provides a large-order analysis of the CMX for the Rabi Hamiltonian, demonstrating its limitations and oscillatory behavior.

Findings

CMX exhibits oscillations at large orders

CMX is unreliable for practical use

Large-order moments were computed successfully

Abstract

We analyze the convergence properties of the connected moments expansion (CMX) for the Rabi Hamiltonian. To this end we calculate the moments and connected moments of the Hamiltonian operator to a sufficiently large order. Our large--order results suggest that the CMX is not reliable for most practical purposes because the expansion exhibits considerable oscillations.