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

We investigate the relation between non-local and energetic properties in two-dimensional quantum systems of zero-temperature bosons. By analyzing numerous interaction potentials across densities spanning from perturbative to the 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 the 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, 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.