Complete-Graph Tensor Network States: A New Fermionic Wave Function Ansatz for Molecules

TL;DR

This paper introduces the Complete-Graph Tensor Network (CGTN) ansatz, a novel wave function representation for molecules that efficiently captures electron correlation without bias towards a reference state, enabling accurate energy calculations.

Contribution

The paper presents the CGTN ansatz, a new tensor network approach that reduces variational parameters and accurately approximates molecular ground states without reference bias.

Findings

CGTN accurately approximates FCI coefficients for molecules.

CGTN provides reliable energy differences between states.

Application to methylene and ozone demonstrates effectiveness.

Abstract

We present a new class of tensor network states that are specifically designed to capture the electron correlation of a molecule of arbitrary structure. In this ansatz, the electronic wave function is represented by a Complete-Graph Tensor Network (CGTN) ansatz which implements an efficient reduction of the number of variational parameters by breaking down the complexity of the high-dimensional coefficient tensor of a full-configuration-interaction (FCI) wave function. We demonstrate that CGTN states approximate ground states of molecules accurately by comparison of the CGTN and FCI expansion coefficients. The CGTN parametrization is not biased towards any reference configuration in contrast to many standard quantum chemical methods. This feature allows one to obtain accurate relative energies between CGTN states which is central to molecular physics and chemistry. We discuss the implications for quantum chemistry and focus on the spin-state problem. Our CGTN approach is applied to the energy splitting of states of different spin for methylene and the strongly correlated ozone molecule at a transition state structure. The parameters of the tensor network ansatz are variationally optimized by means of a parallel-tempering Monte Carlo algorithm.