  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.
