We employ a mathematical framework based on the Riemann-Hilbert approach developed by Bettelheim et al (2022 J. Phys. A: Math. Gen. 55 135001) to study logarithmic negativity of two intervals of free fermions in the case where the size of the intervals as well as the distance between them is macroscopic. We find that none of the eigenvalues of the density matrix become negative, but rather they develop a small imaginary value, leading to non-zero logarithmic negativity. As an example, we compute negativity at half-filling and for intervals of equal size we find a result of order ( log ( N ) ) − 1 , where N is the typical length scale in units of the lattice spacing. One may compute logarithmic negativity in further situations, but we find that the results are non-universal, depending non-smoothly on the Fermi level and the size of the intervals in units of the lattice spacing.
|Original language||American English|
|Journal||Journal of Physics A: Mathematical and Theoretical|
|State||Published - 10 Nov 2023|
Bibliographical notePublisher Copyright:
© 2023 The Author(s). Published by IOP Publishing Ltd.
- entanglement measures
- Fisher-Hartwig theorem
- logarithmic negativity
- Riemann-Hilbert problem