A Special Case Of A Conjecture By Widom With Implications To Fermionic Entanglement Entropy
Mathematical Physics
2011-07-14 v2 Other Condensed Matter
General Relativity and Quantum Cosmology
High Energy Physics - Theory
math.MP
Spectral Theory
Abstract
We prove a special case of a conjecture in asymptotic analysis by Harold Widom. More precisely, we establish the leading and next-to-leading term of a semi-classical expansion of the trace of the square of certain integral operators on the Hilbert space . As already observed by Gioev and Klich, this implies that the bi-partite entanglement entropy of the free Fermi gas in its ground state grows at least as fast as the surface area of the spatially bounded part times a logarithmic enhancement.
Cite
@article{arxiv.0906.4946,
title = {A Special Case Of A Conjecture By Widom With Implications To Fermionic Entanglement Entropy},
author = {R. C. Helling and H. Leschke and W. L. Spitzer},
journal= {arXiv preprint arXiv:0906.4946},
year = {2011}
}
Comments
20 pages, 3 figures, improvement of the presentation, some references added or updated, proof of Theorem 12 (formerly Lemma 11) added