Eigenvector continuation for the pairing Hamiltonian

TL;DR

This paper demonstrates that eigenvector continuation can effectively emulate and resum perturbative expansions for the pairing Hamiltonian, accurately predicting ground-state energies and phase transitions with minimal training data.

Contribution

It applies eigenvector continuation to the pairing Hamiltonian, showing its effectiveness in resumming perturbation theory and predicting phase transitions with few training points.

Findings

EC-resummed perturbation theory agrees qualitatively with exact solutions.

EC-based emulators accurately predict ground-state energies.

Phase transition is quantitatively captured with minimal training data.

Abstract

The development of emulators for the evaluation of many-body observables has gained increasing attention over the last years. In particular the framework of eigenvector continuation (EC) has been identified as a powerful tool when the Hamiltonian admits for a parametric dependence. By training the emulator on a set of training data the many-body solution for arbitrary parameter values can be robustly predicted in many cases. Furthermore, it can be used to resum perturbative expansions that otherwise diverge. In this work, we apply EC to the pairing Hamiltonian and show that EC-resummed perturbation theory is in qualitative agreement with the exact solution and that EC-based emulators robustly predict the ground-state energy once the training data are chosen appropriately. In particular the phase transition from the normal to the superfluid regime is quantitatively predicted using a very low number of training points.