Universality of charge transport: an approach to SEP in random unitary circuits

We investigate the full counting statistics (FCS) of charge transport in U(1) conserving random unitary circuits. We consider an initial mixed state prepared with different chemical potentials in the left and right half of the system and study the FCS of the charge transferred across the central bond, finding a hydrodynamic approach to the counting statistics of a symmetric simple exclusion process (SEP). This approach is seen in TEBD simulations with an effective statistical mechanics model. To understand this approach analytically, we propose an effective stochastic model for the computation of higher order cumulants.