We consider the macroscopic system of free lattice fermions in one dimension assuming that the one-body Hamiltonian of the system is the one dimensional discrete Schrödinger operator with independent identically distributed random potential. We show analytically and numerically that the variance of the entanglement entropy of the segment $[-M,M]$ of the system is bounded away from zero as $M\rightarrow \infty $. This manifests the absence of the selfaveraging property of the entanglement entropy in our model, meaning that in the one-dimensional case the complete description of the entanglement entropy is provided by its whole probability distribution. This also may be contrasted the case of dimension two or more, where the variance of the entanglement entropy per unit surface area vanishes as $% M\rightarrow \infty $ \cite{El-Co:17}, thereby guaranteeing the representativity of its mean for large $M$ in the multidimensional case.We consider the macroscopic system of free lattice fermions in one dimension assuming that the one-body Hamiltonian of the system is the one dimensional discrete Schrödinger operator with independent identically distributed random potential. We show analytically and numerically that the variance of the entanglement entropy of the segment $[-M,M]$ of the system is bounded away from zero as $M\rightarrow \infty $. This manifests the absence of the selfaveraging property of the entanglement entropy in our model, meaning that in the one-dimensional case the complete description of the entanglement entropy is provided by its whole probability distribution. This also may be contrasted the case of dimension two or more, where the variance of the entanglement entropy per unit surface area vanishes as $% M\rightarrow \infty $ \cite{El-Co:17}, thereby guaranteeing the representativity of its mean for large $M$ in the multidimensional case.

arXiv:1703.08209Mar 23, 20171 citation

Calculation of Entanglement Entropy in Fermion Lattices

Michelle Storms, Rajiv R. P. Singh

Bulletin of the American Physical SocietyOct 4, 20130 citations

Exploring entanglement characteristics in disordered free fermion systems through random bi-partitioning

Mohammad Pouranvari

This study investigates the entanglement properties of disordered free fermion systems undergoing an Anderson phase transition from a delocalized to a localized phase. The entanglement entropy is employed to quantify the degree of entanglement, with the system randomly divided into two subsystems. To explore this phenomenon, one-dimensional tight-binding fermion models and Anderson models in one, two, and three dimensions are utilized. Comprehensive numerical calculations reveal that the entanglement entropy, determined using random bi-partitioning, follows a volume-law scaling in both the delocalized and localized phases, expressed as [Formula: see text], where D represents the dimension of the system. Furthermore, the role of short and long-range correlations in the entanglement entropy and the impact of the distribution of subsystem sites are analyzed.This study investigates the entanglement properties of disordered free fermion systems undergoing an Anderson phase transition from a delocalized to a localized phase. The entanglement entropy is employed to quantify the degree of entanglement, with the system randomly divided into two subsystems. To explore this phenomenon, one-dimensional tight-binding fermion models and Anderson models in one, two, and three dimensions are utilized. Comprehensive numerical calculations reveal that the entanglement entropy, determined using random bi-partitioning, follows a volume-law scaling in both the delocalized and localized phases, expressed as [Formula: see text], where D represents the dimension of the system. Furthermore, the role of short and long-range correlations in the entanglement entropy and the impact of the distribution of subsystem sites are analyzed.

arXiv:2208.11409Modern Physics Letters AFeb 20, 20241 citation

Area Law Scaling for the Entropy of Disordered Quasifree Fermions

Leonid Andreevich Pastur, Victor V. Slavin

We study theoretically and numerically the entanglement entropy of the $d$ -dimensional free fermions whose one-body Hamiltonian is the Anderson model. Using the basic facts of the exponential Anderson localization, we show first that the disorder averaged entanglement entropy $⟨{S}_{\mathrm{\ensuremath{\Lambda}}}⟩$ of the $d$ dimension cube $\mathrm{\ensuremath{\Lambda}}$ of side length $l$ admits the area law scaling $⟨{S}_{\mathrm{\ensuremath{\Lambda}}}⟩\ensuremath{\sim}{l}^{(d\ensuremath{-}1)},l\ensuremath{\gg}1$, even in the gapless case, thereby manifesting the area law in the mean for our model. For $d=1$ and $l\ensuremath{\gg}1$ we obtain then asymptotic bounds for the entanglement entropy of typical realizations of disorder and use them to show that the entanglement entropy is not self-averaging, i.e., has nonvanishing random fluctuations even if $l\ensuremath{\gg}1$.We study theoretically and numerically the entanglement entropy of the $d$-dimensional free fermions whose one-body Hamiltonian is the Anderson model. Using the basic facts of the exponential Anderson localization, we show first that the disorder averaged entanglement entropy $⟨{S}_{\mathrm{\ensuremath{\Lambda}}}⟩$ of the $d$ dimension cube $\mathrm{\ensuremath{\Lambda}}$ of side length $l$ admits the area law scaling $⟨{S}_{\mathrm{\ensuremath{\Lambda}}}⟩\ensuremath{\sim}{l}^{(d\ensuremath{-}1)},l\ensuremath{\gg}1$, even in the gapless case, thereby manifesting the area law in the mean for our model. For $d=1$ and $l\ensuremath{\gg}1$ we obtain then asymptotic bounds for the entanglement entropy of typical realizations of disorder and use them to show that the entanglement entropy is not self-averaging, i.e., has nonvanishing random fluctuations even if $l\ensuremath{\gg}1$.

arXiv:1408.2570Physical Review LettersOct 9, 201454 citations

Entanglement entropy, the reduced density matrices of free fermions, and beyond

Pasquale Calabrese

Journal of Physics A Mathematical and TheoreticalSep 23, 201612 citations

[-M,M]

of the system is bounded away from zero as $M\rightarrow \infty $. This manifests the absence of the selfaveraging property of the entanglement entropy in our model, meaning that in the one-dimensional case the complete description of the entanglement entropy is provided by its whole probability distribution. This also may be contrasted the case of dimension two or more, where the variance of the entanglement entropy per unit surface area vanishes as $% M\rightarrow \infty $ \cite{El-Co:17}, thereby guaranteeing the representativity of its mean for large

M

in the multidimensional case.

We study theoretically and numerically the entanglement entropy of the

d

-dimensional free fermions whose one-body Hamiltonian is the Anderson model. Using the basic facts of the exponential Anderson localization, we show first that the disorder averaged entanglement entropy $⟨{S}_{\mathrm{\ensuremath{\Lambda}}}⟩$ of the

d

dimension cube $\mathrm{\ensuremath{\Lambda}}$ of side length

l

admits the area law scaling $⟨{S}_{\mathrm{\ensuremath{\Lambda}}}⟩\ensuremath{\sim}{l}^{(d\ensuremath{-}1)},l\ensuremath{\gg}1$, even in the gapless case, thereby manifesting the area law in the mean for our model. For

d=1

and $l\ensuremath{\gg}1$ we obtain then asymptotic bounds for the entanglement entropy of typical realizations of disorder and use them to show that the entanglement entropy is not self-averaging, i.e., has nonvanishing random fluctuations even if $l\ensuremath{\gg}1$.