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

Free fermions on a line: asymptotics of the entanglement entropy and entanglement spectrum from full counting statistics