The Absence of the Selfaveraging Property of the Entanglement Entropy of Disordered Free Fermions in One Dimension

Pastur, L. А.; Slavin, V. V.

doi:10.1007/s10955-017-1929-1

Cited by 12 publications

(12 citation statements)

References 42 publications

(121 reference statements)

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“…An area law also holds if H models a particle in a constant magnetic field [LSS20]. Area laws are proven to occur for random Schrödinger operators and Fermi energies in the region of dynamical localisation [PS14,EPS17,PS18a]. The proofs rely on the exponential decay in space of the Fermi projection for E in the region of complete localisation.…”

Section: Introduction and Resultsmentioning

confidence: 99%

How Much Delocalisation is Needed for an Enhanced Area Law of the Entanglement Entropy?

Müller

Pastur

Schulte

2019

Commun. Math. Phys.

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We consider a multi-dimensional continuum Schrödinger 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 upper bound is to use a limiting absorption principle for such kinds of Schrödinger operators.

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Section: Introduction and Resultsmentioning

confidence: 99%

How Much Delocalisation is Needed for an Enhanced Area Law of the Entanglement Entropy?

Müller

Pastur

Schulte

2019

Commun. Math. Phys.

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“…An area law also holds if H models a particle in a constant magnetic field [9,22]. Area laws are proven to occur for random Schrödinger operators and Fermi energies in the region of dynamical localisation [10,25,26]. The proofs rely on the exponential decay in space of the Fermi projection for E in the region of complete localisation.…”

Section: Introduction and Resultsmentioning

confidence: 99%

Stability of the Enhanced Area Law of the Entanglement Entropy

Müller

Schulte

2020

Ann. Henri Poincaré

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We consider a multi-dimensional continuum Schrödinger operator which is given by a perturbation of the negative Laplacian by a compactly supported potential. We establish both an upper bound 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 upper bound is to use a limiting absorption principle for such kinds of Schrödinger operators.

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“…On the other hand, the order of magnitude and the form of the subleading term depend on the "amount of randomness" of an ergodic potential and on the smoothness of ϕ and, especially, a, see e.g. [6,8,11,15,22,27] for recent problems and results.…”

Section: Problem and Resultsmentioning

confidence: 99%

Szegö-type Theorems for One-Dimensional Schrodinger Operator with Random Potential (smooth case)

Pastur¹,

Shcherbina²

2018

Preprint

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The paper is a continuation of work [15] in which the general setting for analogs of the Szegö theorem for ergodic operators was given and several interesting cases were considered.Here we extend the results of [15] to a wider class of test functions and symbols which determine the Szegö-type asymptotic formula for the one-dimensional Schrodinger operator with random potential. We show that in this case the subleading term of the formula is given by a Central Limit Theorem in the spectral context, hence the term is asymptotically proportional to L 1/2 , where L is the length of the interval on which the Schrodinger operator is initially defined. This has to be compared with the classical Szegö formula, where the subleading term is bounded in L, L → ∞. We prove an analog of standard Central Limit Theorem (the convergence of the probability of the corresponding event to the Gaussian Law) as well as an analog of the almost sure Central Limit Theorem (the convergence with probability 1 of the logarithmic means of the indicator of the corresponding event to the Gaussian Law). We illustrate our general results by establishing the asymptotic formula for the entanglement entropy of free disordered Fermions for non-zero temperature.

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The Absence of the Selfaveraging Property of the Entanglement Entropy of Disordered Free Fermions in One Dimension

Cited by 12 publications

References 42 publications

How Much Delocalisation is Needed for an Enhanced Area Law of the Entanglement Entropy?

How Much Delocalisation is Needed for an Enhanced Area Law of the Entanglement Entropy?

Stability of the Enhanced Area Law of the Entanglement Entropy

Szegö-type Theorems for One-Dimensional Schrodinger Operator with Random Potential (smooth case)

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