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We investigate the fluctuations of the spin current for the one dimensionalXX spin chain starting from the domain wall initial condition. The generatingfunction of the current is shown to be written as a determinant with the Besselkernel. An exact analytical expression for the large deviation function isobtained by applying the Coulomb gas method. Our results are also compared withDMRG calculations.

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