Flexible Ansatz for N-body Perturbation Theory

TL;DR

The paper introduces FANPT, a versatile perturbation theory framework for solving the Schrödinger equation for complex wavefunctions, building on FANCI, and demonstrating its stability across various challenging conditions.

Contribution

It presents a new flexible perturbation theory method, FANPT, that extends previous work on FANCI to handle arbitrary wavefunctions and orders, with proven stability.

Findings

FANPT equations are well-behaved across diverse conditions.

FANPT effectively handles static correlation and non-linear wavefunctions.

Recursive expressions enable systematic perturbation order expansion.

Abstract

We propose a new Perturbation Theory framework that can be used to help with the projective solution of the Schr\"odinger equation for arbitrary wavefunctions. This Flexible Ansatz for N-body Perturbation Theory (FANPT) is based on our previously proposed Flexible Ansatz for N-body Configuration Interaction (FANCI). We derive recursive FANPT expressions including arbitrary orders in the perturbation hierarchy. We show that the FANPT equations are well-behaved across a wide range of conditions, including static correlation-dominated configurations and highly non-linear wavefunctions.