Cluster many-body expansion: a many-body expansion of the electron correlation energy about a cluster mean-field reference

TL;DR

This paper introduces the cluster many-body expansion (cMBE), a novel method for efficiently calculating correlation energies in large, strongly correlated systems by partitioning active spaces and using a tensor product state reference.

Contribution

The paper extends the many-body expansion approach to tensor product state wavefunctions, improving convergence and enabling calculations on large, complex systems.

Findings

cMBE improves convergence at lower orders compared to traditional MBE.

Successfully applied to Hubbard models and chromium dimer, demonstrating accuracy.

Enabled analysis of a large graphene nano-sheet with 114 electrons and orbitals.

Abstract

The many-body expansion (MBE) is an efficient tool which has a long history of use for calculating interaction energies, binding energies, lattice energies, and so on. In the past, applications of MBE to correlation energy have been unfeasible for large systems, but recent improvements to computing resources have sparked renewed interest in capturing the correlation energy using the generalized $n$-th order Bethe-Goldstone equation. In this work, we extend this approach, originally proposed for a Slater determinant, to a tensor product state (TPS) based wavefunction. By partitioning the active space into smaller orbital clusters, our approach starts from a cluster mean field reference TPS configuration and includes the correlation contribution of the excited TPSs using the many-body expansion. This method, named cluster many-body expansion (cMBE), improves the convergence of MBE at lower orders compared to directly doing a block based MBE from a RHF reference. We present numerical results for strongly correlated systems such as the one- and two-dimensional Hubbard models and the chromium dimer. The performance of the cMBE method is also tested by partitioning the extended $\pi$ space of several large $\pi$-conjugated systems, including a graphene nano-sheet with a very large active space of 114 electrons in 114 orbitals, which would require $10^{66}$ determinants for the exact FCI solution.