Coupled cluster and perturbation theories based on a cluster mean-field reference applied to strongly correlated spin systems

TL;DR

This paper develops perturbation and coupled-cluster theories based on a cluster mean-field reference to accurately describe ground states of strongly-correlated spin systems, demonstrated on Heisenberg models.

Contribution

It introduces a novel cluster mean-field approach combined with perturbation and coupled-cluster theories for strongly-correlated spins.

Findings

Cluster-based methods yield accurate energies for 1D and 2D Heisenberg models.

Extrapolation scheme effectively estimates thermodynamic limit energies.

Correlated methods perform well with sufficiently large clusters.

Abstract

We introduce perturbation and coupled-cluster theories based on a cluster mean-field reference for describing the ground state of strongly-correlated spin systems. In cluster mean-field, the ground state wavefunction is written as a simple tensor product of optimized cluster states. The cluster language and the mean-field nature of the ansatz allows for a straightforward improvement which uses perturbation theory and coupled-cluster to account for inter-cluster correlations. We present benchmark calculations on the 1D chain and 2D square $J_1-J_2$ Heisenberg model, using cluster mean-field, perturbation theory and coupled-cluster. We also present an extrapolation scheme that allows us to compute thermodynamic limit energies accurately. Our results indicate that, with sufficiently large clusters, the correlated methods (cPT2, cPT4 and cCCSD) can provide a relatively accurate description of the Heisenberg model in the regimes considered, which suggests that the methods presented can be used for other strongly-correlated systems. Some ways to improve upon the methods presented in this work are discussed.