We calculate the full counting statistics (FCS) of a subsystem energy in freefermionic systems by means of the Grassmann variables. We demonstrate that thegenerating function of these systems can be written as a determinant formulawith respect to the Hamiltonian couplings and by employing the Bell'spolynomials, we derive exact formulas for the subsystem energy moments. Inaddition, we discuss the same quantities in the quantum XY spin chain, and wedemonstrate that at the critical regimes the fluctuations of the energy momentsdecay like a power-law as we expect from the conformal field theory arguments,while in non-critical regimes, the decay is exponential. Furthermore, wediscuss the full counting statistics of subsystem energy in the quantum XXchain.
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