Abstract
Measuring physical observables requires averaging experimental outcomes over numerous identical measurements. The complete distribution function of possible outcomes or its Fourier transform, known as the full counting statistics, provides a more detailed description. This method captures the fundamental quantum fluctuations in many-body systems and has gained significant attention in quantum transport research. In this letter, we propose that cusp singularities in the full counting statistics are a novel tool for distinguishing between ordered and disordered phases. As a specific example, we focus on the superfluid-to-Mott transition in the Bose-Hubbard model and introduce Z_A(α)= exp(iα Σ_i∈ A(n_i-n)) with n= n_i . Through both analytical analysis and numerical simulations, we demonstrate that ∂_α log Z_A(α) exhibits a discontinuity near α=π in the superfluid phase when the subsystem size is sufficiently large, while it remains smooth in the Mott phase. This discontinuity can be interpreted as a first-order transition between different semi-classical configurations of vortices. We anticipate that our discoveries can be readily tested using state-of-the-art ultracold atom and superconducting qubit platforms.