A phenomenological universal expression for the condensate fraction in strongly-correlated two-dimensional Bose gases

TL;DR

This paper introduces a universal phenomenological expression linking the condensate fraction to kinetic and quantum energies in 2D strongly-correlated Bose gases, validated by simulations and applicable to various quantum systems.

Contribution

The authors propose a novel universal relation for the condensate fraction in 2D Bose gases, validated across different interaction regimes and systems, including liquid helium and TMDC materials.

Findings

Quantum Monte Carlo simulations confirm the analytical expression.

The relation applies to both perturbative and strongly correlated regimes.

Potential relevance to experiments with excitons and ultracold atoms.

Abstract

We investigate the relation between non-local and energetic properties in 2D quantum systems of zero-temperature bosons. By analyzing numerous interaction potentials across densities spanning from perturbative to strongly correlated regime, we discover a novel high-precision quantum phenomenological universality: the condensate fraction can be expressed through kinetic energy and quantum energy, defined as total energy relative to classical crystal state. Quantum Monte Carlo simulations accurately validate our analytical expression. Furthermore, we test the obtained relation on the fundamental example of a non-perturbative system, namely, the liquid helium. The proposed relation is relevant to experiments with excitons in transition metal dichalcogenides (TMDC) materials, as well as ultracold atoms and other quantum systems in reduced dimensionality.