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

Abstract

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.

6 pages, comparison with numerics added, published version

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• Symmetry-resolved entanglement entropy in critical free-fermion chains
• Full counting statistics and symmetry resolved entanglement for free conformal theories with interface defects
• Rényi entropy flows from quantum heat engines
• Entanglement entropy in Fermi gases and Anderson's orthogonality catastrophe
• Distinguishing Quantum Phases through Cusps in Full Counting Statistics
• Zero-mode entanglement across a conformal defect
• Entanglement Hamiltonian of a nonrelativistic Fermi gas
• Measuring full counting statistics in a trapped-ion quantum simulator
• Effect of Single Impurity on Free Fermion Entanglement Entropy
• Universal entanglement signatures of quantum liquids as a guide to fermionic criticality
• Entanglement entropies of an interval in the free Schrödinger field theory on the half line
• Entanglement entropies of an interval in the free Schrödinger field theory at finite density