Theoretical approaches to liquid Helium

TL;DR

This paper reviews the main theoretical methods used to study liquid Helium from a microscopic perspective, highlighting variational and stochastic approaches and their contributions to understanding this strongly quantum many-body system.

Contribution

It provides a comprehensive overview of the variational and stochastic methods applied to liquid Helium, emphasizing recent progress and methodological accuracy.

Findings

High accuracy variational methods achieved

Effective stochastic techniques discussed

Strong link between Helium studies and quantum many-body methods

Abstract

In this article, we review the main theoretical methods applied to the study of liquid Helium adopting a microscopic approach, that is, starting from the many-particle Hamiltonian of the system. Following an introduction on the first early approaches, we discuss two main issues. In the first one, we report the main ingredients of a theoretical approach based on the variational method, with the discussion of the high accuracy obtained with them and the related progress in the design of highly accurate trial wave functions. In the second part, the main stochastic methods used in this study are briefly discussed. Altogether reflects the strong links between the study of liquid Helium and the progress in the development of new and extremely powerful approaches to deal with one of the most strongly quantum many-body systems in Nature.