Optimizing linked cluster expansions by white graphs

TL;DR

This paper presents a white graph expansion technique for linked cluster calculations in perturbative continuous unitary transformations, reducing computational complexity for models with many couplings.

Contribution

It introduces an optimized bookkeeping method exploiting model-independent Hamiltonians, significantly decreasing relevant graph counts in complex microscopic models.

Findings

Effective for models with numerous coupling constants

Reduces the number of relevant graphs drastically

Demonstrated on a 2D quantum spin model

Abstract

We introduce a white graph expansion for the method of perturbative continuous unitary transformations when implemented as a linked cluster expansion. The essential idea behind an expansion in white graphs is to perform an optimized bookkeeping during the calculation by exploiting the model-independent effective Hamiltonian in second quantization and the associated inherent cluster additivity. This appoach is shown to be especially well suited for microscopic models with many coupling constants, since the total number of relevant graphs is drastically reduced. The white graph expansion is exemplified for a two-dimensional quantum spin model of coupled two-leg XXZ ladders.