  We consider the entanglement entropy for a line segment in the system of
noninteracting one-dimensional fermions at zero temperature. In the limit of a
large segment length L, the leading asymptotic behavior of this entropy is
known to be logarithmic in L. We study finite-size corrections to this
asymptotic behavior. Based on an earlier conjecture of the asymptotic expansion
for full counting statistics in the same system, we derive a full asymptotic
expansion for the von Neumann entropy and obtain first several corrections for
the Renyi entropies. Our corrections for the Renyi entropies reproduce earlier
results. We also discuss the entanglement spectrum in this problem in terms of
single-particle occupation numbers.
