Strong electronic correlation in the Hydrogen chain: a variational Monte Carlo study

TL;DR

This study uses variational Monte Carlo to accurately analyze strong electronic correlations in a hydrogen chain, demonstrating its effectiveness compared to traditional quantum chemistry methods especially near phase transitions.

Contribution

It introduces a highly accurate variational Monte Carlo approach with a Jastrow-antisymmetrized geminal wave function for the hydrogen chain, capturing correlation effects near phase transitions.

Findings

Achieved accuracy comparable to density matrix renormalization group calculations.

Characterized the crossover between weakly and strongly correlated regimes.

Validated variational Monte Carlo as a flexible alternative for strongly correlated systems.

Abstract

In this article, we report a fully ab initio variational Monte Carlo study of the linear, and periodic chain of Hydrogen atoms, a prototype system providing the simplest example of strong electronic correlation in low dimensions. In particular, we prove that numerical accuracy comparable to that of benchmark density matrix renormalization group calculations can be achieved by using a highly correlated Jastrow-antisymmetrized geminal power variational wave function. Furthermore, by using the so-called "modern theory of polarization" and by studying the spin-spin and dimer-dimer correlations functions, we have characterized in details the crossover between the weakly and strongly correlated regimes of this atomic chain. Our results show that variational Monte Carlo provides an accurate and flexible alternative to highly correlated methods of quantum chemistry which, at variance with these methods, can be also applied to a strongly correlated solid in low dimensions close to a crossover or a phase transition.