Exploring non-linear correlators on AGP

TL;DR

This paper investigates non-linear exponential correlator methods on antisymmetrized geminal power (AGP) references, demonstrating their summability and benchmarking their performance on pairing Hamiltonian ground states.

Contribution

It introduces two novel non-linear exponential ansatze for AGP, including a summable similarity transformed Hamiltonian and a quantum-inspired unitary pair-hopper approach.

Findings

Summation of the similarity transformed Hamiltonian is feasible and accurate.

Benchmark results show promising performance on pairing Hamiltonian ground states.

The methods extend AGP's applicability to strongly correlated systems.

Abstract

Single-reference methods such as Hartree-Fock-based coupled cluster theory are well known for their accuracy and efficiency for weakly correlated systems. For strongly correlated systems, more sophisticated methods are needed. Recent studies have revealed the potential of the antisymmetrized geminal power (AGP) as an excellent initial reference for the strong correlation problem. While these studies improved on AGP by linear correlators, we explore some non-linear exponential ansatze in this paper. We investigate two approaches in particular. Similar to Phys. Rev. B 91, 041114(R) (2015), we show that the similarity transformed Hamiltonian with a Hilbert-space Jastrow operator is summable to all orders and can be solved over AGP by projecting Schrodinger's equation. The second approach is based on approximating the unitary pair-hopper ansatz recently proposed for application on a quantum computer. We report benchmark numerical calculations against the ground state of the pairing Hamiltonian for both of these approaches.