Computer aided perturbation theory by cumulants: dimerized and frustrated spin 1/2 chain

TL;DR

This paper introduces a cumulant-based, computer-aided perturbation theory applicable to complex quantum systems, demonstrated on spin chains, allowing calculations beyond traditional limitations.

Contribution

It presents a novel cumulant approach for perturbation theory that applies to systems with arbitrary Hilbert spaces, unlike previous methods.

Findings

Ground state energy calculated up to seventh order.

Method applicable to systems with arbitrary Hilbert spaces.

Effective for dimerized and frustrated spin chains.

Abstract

This paper demonstrates that a computer aided perturbation theory can easily be realized by use of a cumulant approach. In contrast to a recent alternative formulation on the basis of Wegner's flow equation method the present approach can be applied to systems with arbitrary Hilbert space. In particular an equidistant spectrum of the unperturbed part of the Hamiltonian is not needed. The method is illustrated in detail for dimerized and frustrated spin 1/2 chains for which the ground state energy is calculated up to seventh order perturbation theory.