# Diagrammatic Coupled Cluster Monte Carlo

## TL;DR

This paper introduces diagCCMC, a modified coupled cluster Monte Carlo method that efficiently samples connected terms, significantly reducing memory costs and enabling accurate simulations of strongly correlated systems.

## Contribution

The paper presents diagCCMC, a novel stochastic algorithm that samples only connected components of the similarity-transformed Hamiltonian, improving memory efficiency in coupled cluster Monte Carlo methods.

## Key findings

- Memory cost scales linearly with system size for local, noninteracting systems.
- Significant memory reduction observed during dissociation of helium chains.
- Method remains stable and accurate for strongly correlated molecules like stretched N₂.

## Abstract

We propose a modified coupled cluster Monte Carlo algorithm that stochastically samples connected terms within the truncated Baker--Campbell--Hausdorff expansion of the similarity transformed Hamiltonian by construction of coupled cluster diagrams on the fly. Our new approach -- diagCCMC -- allows propagation to be performed using only the connected components of the similarity-transformed Hamiltonian, greatly reducing the memory cost associated with the stochastic solution of the coupled cluster equations. We show that for perfectly local, noninteracting systems, diagCCMC is able to represent the coupled cluster wavefunction with a memory cost that scales linearly with system size. The favorable memory cost is observed with the only assumption of fixed stochastic granularity and is valid for arbitrary levels of coupled cluster theory. Significant reduction in memory cost is also shown to smoothly appear with dissociation of a finite chain of helium atoms. This approach is also shown not to break down in the presence of strong correlation through the example of a stretched nitrogen molecule. Our novel methodology moves the theoretical basis of coupled cluster Monte Carlo closer to deterministic approaches.