Exact large deviation function of spin current for the one dimensional XX spin chain with domain wall initial condition

We investigate the fluctuations of the spin current for the one-dimensional XX spin chain starting from the domain wall initial condition. The generating function of the current is shown to be written as a determinant with the Bessel kernel. An exact analytical expression for the large deviation function is obtained by applying the Coulomb gas method. Our results are also compared with DMRG calculations.