We consider one-dimensional quantum spin chain, which is called XX model (XX0 model or isotropic XY model) in a transverse magnetic field. We study the model on the infinite lattice at zero temperature. We are interested in the entropy of a subsystem [a block of L neighboring spins] it describes entanglement of the block with the rest of the ground state. For large blocks entropy scales logarithmically [10,11]. We prove the logarithmic formula for the leading term and calculate the next term. We discovered that the dependence on the magnetic field interacting with spins is very simple: the magnetic field effectively reduce the size of the subsystem. We also calculate entropy of a subsystem of a small size.We also evaluated Rényi and Tsallis entropies of the subsystem. We represented the entropy in terms of a Toeplitz determinant and calculated the asymptotic analytically.

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