Projective approach to the entanglement entropy of 1-$d$ fermions

Physics – Condensed Matter – Statistical Mechanics

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

10 pages, 6 figures; added discussion section; accepted Phys. Rev. B

Scientific paper

The entanglement entropy of two gapless non-interacting fermion subsystems is computed approximately in a way that avoids the introduction of replicas and a geometric interpretation of the reduced density matrix. We exploit the similarity between the Schmidt basis wavefunction and superfluid BCS wavefunction and compute the entropy using the BCS approximation. Within this analogy, the Cooper pairs are particle-hole pairs straddling the boundary and the effective interaction between them is induced by the projection of the Hilbert space onto the incomplete Schmidt basis. The resulting singular interaction may be thought of as "lifting" the degeneracy of the single particle distribution function. For two coupled fermion systems of linear size $L$, we solve the BCS gap equation approximately to find the entropy $S \approx (w^2/t^2)\log{L}$ where $w$ is the hopping amplitude at the boundary of the subsystem and $2t$ is the bandwidth. We further interpret this result based upon the relationship between entanglement spectrum, entropy and number fluctuations.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Projective approach to the entanglement entropy of 1-$d$ fermions 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 Projective approach to the entanglement entropy of 1-$d$ fermions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Projective approach to the entanglement entropy of 1-$d$ fermions will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-508417

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.