Particle number fluctuations in one dimensional quantum liquids

In quantum many-body systems, the careful treatment of particle number plays a central role in determining the accessible physics. Although the canonical and grand canonical ensembles both describe equilibrium, their distinct constraints can lead to meaningful differences in finite systems, especially in one spatial dimension where quantum and thermal fluctuations are enhanced. To probe the interplay between number fluctuations and strong correlations, we analytically compute grand canonical corrections to the density–density (pair) correlation function of a Tomonaga–Luttinger liquid via bosonization. We identify a regime where these corrections are non-negligible and benchmark our findings using an exactly solvable model of bosons with contact interactions in one dimension. The results may have implications for experiments on confined quantum liquids with tunable density.