Entanglement Entropy of Fermi Liquids via Multi-dimensional Bosonization

Details Entanglement Entropy of Fermi Liquids via Multi-dimensional Bosonization Entanglement Entropy of Fermi Liquids via Multi-dimensional Bosonization

2011-10-13

arxiv.org/abs/1110.3004v3

Phys. Rev. X 2, 011012 (2012)

Physics

Condensed Matter

Statistical Mechanics

18 pages, accepted version with major update

Scientific paper

10.1103/PhysRevX.2.011012

The logarithmic violations of the area law, i.e. an "area law" with logarithmic correction of the form $S \sim L^{d-1} \log L$, for entanglement entropy are found in both 1D gapless system and for high dimensional free fermions. The purpose of this work is to show that both violations are of the same origin, and in the presence of Fermi liquid interactions such behavior persists for 2D fermion systems. In this paper we first consider the entanglement entropy of a toy model, namely a set of decoupled 1D chains of free spinless fermions, to relate both violations in an intuitive way. We then use multi-dimensional bosonization to re-derive the formula by Gioev and Klich [Phys. Rev. Lett. 96, 100503 (2006)] for free fermions through a low-energy effective Hamiltonian, and explicitly show the logarithmic corrections to the area law in both cases share the same origin: the discontinuity at the Fermi surface (points). In the presence of Fermi liquid (forward scattering) interactions, the bosonized theory remains quadratic in terms of the original local degrees of freedom, and after regularizing the theory with a mass term we are able to calculate the entanglement entropy perturbatively up to second order in powers of the coupling parameter for a special geometry via the replica trick. We show that these interactions do not change the leading scaling behavior for the entanglement entropy of a Fermi liquid. At higher orders, we argue that this should remain true through a scaling analysis.

Affiliated with

Also associated with

No associations

Rating

Entanglement Entropy of Fermi Liquids via Multi-dimensional Bosonization does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Entanglement Entropy of Fermi Liquids via Multi-dimensional Bosonization, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Entanglement Entropy of Fermi Liquids via Multi-dimensional Bosonization will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-500699