A Special Case Of A Conjecture By Widom With Implications To Fermionic Entanglement Entropy

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 $L^2({\mathbb{R}}^d)$. 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.

20 pages, 3 figures, improvement of the presentation, some references added or updated, proof of Theorem 12 (formerly Lemma 11) added

References in corpus (5)

• Entanglement entropy and conformal field theory
• Reduced density matrices and entanglement entropy in free lattice models
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Entanglement scaling in critical two-dimensional fermionic and bosonic systems
• The modified Newtonian dynamics-MOND-and its implications for new physics

Cited by in corpus (29)

• Quantum entanglement in condensed matter systems
• Exact relations between particle fluctuations and entanglement in Fermi gases
• Scaling of Rényi entanglement entropies of the free Fermi-gas ground state: a rigorous proof
• Symmetry resolved entanglement in two-dimensional systems via dimensional reduction
• Entanglement Entropy of Fermi Liquids via Multi-dimensional Bosonization
• Finite-temperature entanglement negativity of free fermions
• Conformal Field Theory on the Fermi Surface
• Cornering the universal shape of fluctuations
• Entanglement Entropy of Non-Hermitian Free Fermions
• Wiener-Hopf operators in higher dimensions: the Widom conjecture for piece-wise smooth domains
• The negativity contour: a quasi-local measure of entanglement for mixed states
• Stable computation of entanglement entropy for 2D interacting fermion systems
• Entanglement does not generally decrease under renormalization
• Entropy, gap and a multi-parameter deformation of the Fredkin spin chain
• Functions of self-adjoint operators in ideals of compact operators
• Large Block Properties of the Entanglement Entropy of Disordered Fermions
• How much delocalisation is needed for an enhanced area law of the entanglement entropy?
• Bounds on the entanglement entropy of droplet states in the XXZ spin chain
• Quantum entanglement in the one-dimensional spin-orbital SU(2)$\otimes XXZ$ model
• Entanglement entropy of compressible holographic matter: loop corrections from bulk fermions
• The Widom-Sobolev formula for discontinuous matrix-valued symbols
• On a coefficient in trace formulas for Wiener-Hopf operators
• The Fermionic Entanglement Entropy of the Vacuum State of a Schwarzschild Black Hole Horizon
• Free Fermions Violate the Area Law For Entanglement Entropy
• Universal entanglement signatures of quantum liquids as a guide to fermionic criticality
• Trace formulas for Wiener--Hopf operators with applications to entropies of free fermionic equilibrium states
• Quasi-classical asymptotics for pseudo-differential operators with discontinuous symbols: Widom's Conjecture
• On the Szegő formulas for truncated Wiener-Hopf operators
• A Szegő limit theorem for translation-invariant operators on polygons