Capturing long range correlations in two-dimensional quantum lattice systems using correlator product states

TL;DR

This paper evaluates correlator product states for modeling ground states of 2D quantum spin systems, highlighting how different correlator types capture local and long-range correlations effectively depending on the model.

Contribution

It compares plaquette and bond correlator product states in 2D spin models, providing insights into their suitability for different systems and correlations.

Findings

Plaquette correlators estimate energy more accurately in the Ising model.

Bond correlators better capture long-range correlations and critical behavior.

Plaquettes outperform bond correlators for the Heisenberg model due to more local parameters.

Abstract

We study the suitability of correlator product states for describing ground-state properties of two-dimensional spin models. Our ansatz for the many-body wave function takes the form of either plaquette or bond correlator product states and the energy is optimized by varying the correlators using Monte Carlo minimization. For the Ising model we find that plaquette correlators are best for estimating the energy while bond correlators capture the expected long-range correlations and critical behavior of the system more faithfully. For the antiferromagnetic Heisenberg model, however, plaquettes outperform bond correlators at describing both local and long-range correlations because of the substantially larger number of local parameters they contain. These observations have quantitative implications for the application of correlator product states to other more complex systems, and give important heuristic insights: in particular the necessity of carefully tailoring the choice of correlators to the system considered, its interactions and symmetries.