Bipartite particle number fluctuations in dephased long-range lattice systems
We investigate the dynamics of subsystem particle number fluctuations in a long-range system with power-law decaying hopping strength characterized by exponent $μ$ and subjected to a local dephasing at every site. We introduce an efficient {\it bond length} representation for the four-point correlator, enabling the large-scale simulation of the dynamics of particle number fluctuations from translationally invariant initial states. Our results show that the particle number fluctuation dynamics exhibit one-parameter Family-Vicsek scaling, with superdiffusive scaling exponents for $μ< 1.5$ and diffusive scaling exponents for $μ\geq 1.5$. Finally, exploiting the bond-length representation, we provide an exact analytical expression for the particle number fluctuations and their scaling exponents in the short-range limit ($μ\to \infty)$.