Free fermions on a line: Asymptotics of the entanglement entropy and entanglement spectrum from full counting statistics
1 Institute for Theoretical Physics, ETH Zurich - 8093 Zurich, Switzerland
2 Institute for Theoretical Physics, University of Zurich - 8057 Zurich, Switzerland
Received: 19 September 2012
Accepted: 29 November 2012
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 Rényi entropies. Our corrections for the Rényi entropies reproduce earlier results. We also discuss the entanglement spectrum in this problem in terms of single-particle occupation numbers.
PACS: 03.65.Ud – Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.) / 05.30.Fk – Fermion systems and electron gas / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EPLA, 2012