A generalized perspective on non-perturbative linked cluster expansions

TL;DR

This paper addresses the challenge of reduced symmetry in non-perturbative linked cluster expansions for excited states, proposing a generalized cluster additivity and an optimized graph-based continuous unitary transformation scheme.

Contribution

It introduces a new generalized cluster additivity concept and an optimized gCUT scheme that goes beyond using exact eigenvectors, improving understanding of symmetry breaking in NLCEs.

Findings

Identifies fundamental symmetry-breaking challenge in NLCEs for excited states

Develops a generalized cluster additivity framework

Proposes an optimized gCUT scheme that surpasses traditional methods

Abstract

We identify a fundamental challenge for non-perturbative linked cluster expansions (NLCEs) resulting from the reduced symmetry on graphs, most importantly the breaking of translational symmetry, when targeting the properties of excited states. A generalized notion of cluster additivity is introduced, which is used to formulate an optimized scheme of graph-based continuous unitary transformations (gCUTs) allowing to solve and to physically understand this fundamental challenge. Most importantly, it demands to go beyond the paradigm of using the exact eigenvectors on graphs.