# Stability of the Enhanced Area Law of the Entanglement Entropy

@article{Mller2020StabilityOT,
title={Stability of the Enhanced Area Law of the Entanglement Entropy},
author={Peter M{\"u}ller and Ruth Schulte},
journal={arXiv: Mathematical Physics},
year={2020}
}
• Published 6 April 2020
• Mathematics, Physics
• arXiv: Mathematical Physics
We consider a multi-dimensional continuum Schrodinger operator which is given by a perturbation of the negative Laplacian by a compactly supported potential. We establish both an upper and a lower bound on the bipartite entanglement entropy of the ground state of the corresponding quasi-free Fermi gas. The bounds prove that the scaling behaviour of the entanglement entropy remains a logarithmically enhanced area law as in the unperturbed case of the free Fermi gas. The central idea for the…
6 Citations
Lower Bound to the Entanglement Entropy of the XXZ Spin Ring
• Physics
• 2020
We study the free XXZ quantum spin model defined on a ring of size $L$ and show that the bipartite entanglement entropy of eigenstates belonging to the first energy band above the vacuum ground state
Stability of a Szeg\H{o}-type asymptotics
• Mathematics
• 2021
We consider a multi-dimensional continuum Schrodinger operator $H$ which is given by a perturbation of the negative Laplacian by a compactly supported bounded potential. We show that, for a fairly
Entanglement entropy bounds in the higher spin XXZ chain
• Mathematics
Journal of Mathematical Physics
• 2021
We consider the Heisenberg XXZ spin-$J$ chain ($J\in\mathbb{N}/2$) with anisotropy parameter $\Delta$. Assuming that $\Delta>2J$, and introducing threshold energies
On the stability of the area law for the entanglement entropy of the Landau Hamiltonian
Abstract. We consider the two-dimensional ideal Fermi gas subject to a magnetic field which is perpendicular to the Euclidean plane R and whose strength B(x) at x ∈ R converges to some B0 > 0 as ‖x‖
Asymptotic Growth of the Local Ground-State Entropy of the Ideal Fermi Gas in a Constant Magnetic Field
• Mathematics
Communications in Mathematical Physics
• 2020
We consider the ideal Fermi gas of indistinguishable particles without spin but with electric charge, confined to a Euclidean plane $${{\mathbb {R}}}^2$$ R 2 perpendicular to an external constant

## References

SHOWING 1-10 OF 47 REFERENCES
Violation of the entropic area law for fermions.
• M. Wolf
• Physics
Physical review letters
• 2006
It is proven that the presented scaling law holds whenever the Fermi surface is finite, and this is, in particular, true for all ground states of Hamiltonians with finite range interactions.
A Special Case Of A Conjecture By Widom With Implications To Fermionic Entanglement Entropy
• Mathematics
• 2009
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
Area law scaling for the entropy of disordered quasifree fermions.
• Physics
Physical review letters
• 2014
It is shown first that the disorder averaged entanglement entropy of the d dimension cube Λ of side length l admits the area law scaling ⟨S(Λ)⟩ ∼ l((d-1),l ≫ 1, even in the gapless case, thereby manifesting the areaLaw in the mean for the model.
Scaling of Rényi entanglement entropies of the free fermi-gas ground state: a rigorous proof.
• Mathematics, Physics
Physical review letters
• 2014
A complete proof of that formula and of its generalization to Rényi entropies of all orders α>0 and α=1/2 is provided.
From conformal to volume-law for the entanglement entropy in exponentially deformed critical spin 1/2 chains
• Physics
• 2014
An exponential deformation of 1D critical Hamiltonians gives rise to ground states whose entanglement entropy satisfies a volume-law. This effect is exemplified in the XX and Heisenberg models. In
Entanglement entropy of fermions in any dimension and the Widom conjecture.
• Physics
Physical review letters
• 2006
We show that entanglement entropy of free fermions scales faster than area law, as opposed to the scaling L(d-1) for the harmonic lattice, for example. We also suggest and provide evidence in support
How Much Delocalisation is Needed for an Enhanced Area Law of the Entanglement Entropy?
• Physics
Communications in Mathematical Physics
• 2019
We consider the random dimer model in one space dimension with Bernoulli disorder. For sufficiently small disorder, we show that the entanglement entropy exhibits at least a logarithmically enhanced
Random Matrix Theory and Entanglement in Quantum Spin Chains
• Mathematics
• 2004
We compute the entropy of entanglement in the ground states of a general class of quantum spin-chain Hamiltonians — those that are related to quadratic forms of Fermi operators — between the first N
A uniform area law for the entanglement of eigenstates in the disordered XY chain
• Physics
• 2015
We consider the isotropic or anisotropic XY spin chain in the presence of a transversal random magnetic field, with parameters given by random variables. It is shown that eigenfunction correlator
Szegö limit theorem for operators with discontinuous symbols and applications to entanglement entropy
The main result in this paper is a one term Szego type asymptotic formula with a sharp remainder estimate for a class of integral operators of the pseudodifferential type with symbols which are