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.