Entanglement entropy and particle number cumulants of disordered fermions

Burmistrov, I. S.; Tikhonov, Konstantin S.; Gornyi, I. V.; Mirlin, A. D.

doi:10.1016/j.aop.2017.05.011

Cited by 8 publications

(4 citation statements)

References 32 publications

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“…One of the remarkable features of MBL phase is that von Neumann entropy of entanglement [8,9] does not show a volume-law scaling for finite temperatures. Instead of that there is an arealaw behavior of the entropy [10][11][12] which is similar to the low temperature results obtained for the ground state of gapped spin liquids [9]. The recent experimental observations of MBL phase have been reported for fermions in an optical lattice [13], driven dipolar spin impurities in diamond [14] and in a gas of ultracold fermionic potassium atoms [15].…”

Section: Introductionsupporting

confidence: 79%

Many-body synchronization of interacting qubits by engineered ac-driving

Remizov,

Shapiro,

Rubtsov

2017

Preprint

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In this work we introduce the many-body synchronization of an interacting qubit ensemble which allows one to switch dynamically from many-body-localized (MBL) to an ergodic state. We show that applying of π-pulses with altering phases, one can effectively suppress the MBL phase and, hence, eliminate qubits disorder. The findings are based on the analysis of the Loschmidt echo dynamics which shows a transition from a power-law decay to more rapid one indicating the dynamical MBL-to-ergodic transition. The technique does not require to know the microscopic details of the disorder.

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Section: Introductionsupporting

confidence: 79%

Many-body synchronization of interacting qubits by engineered ac-driving

Remizov,

Shapiro,

Rubtsov

2017

Preprint

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“…2) is proportional to the variance of the number of fermions in Λ, see e.g. [18] and references therein. This quantity can also be expressed via the density-density correlator (δ(E ′ − H S )) mn (δ(E ′′ − H S )) nm , important in the solid state theory [29,35].…”

Section: Generalitiesmentioning

confidence: 99%

“…Certain disordered quantum systems have also been considered, mainly various spin chains, and both the one-dimensional area law and the enhanced area law have been found and analyzed, see e.g. [8,10,13,17,18] and references therein.…”

Section: Introductionmentioning

confidence: 99%

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

Pastur

Slavin

2017

J Stat Phys

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We consider the macroscopic system of free lattice fermions in one dimensions assuming that the one-body Hamiltonian of the system is the one dimensional discrete Schrödinger operator with independent identically distributed random potential. We show that the variance of the entanglement entropy of the segment [−M, M ] of the system is bounded away from zero as M → ∞. 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 → ∞ [6], thereby guaranteing the representativity of its mean for large M in the multidimensional case.PACS numbers 03.67. Mn, 03.67, 05.30.Fk, 72.15.Rn

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“…A connection between the summation of a weighted series of cumulants of the number of particles in the sub-system and the entanglement entropy was established by Klich and Levitov [22,23] for non-interacting free fermions. This theory was extended to include disordered systems by Burmistrov et al [24]. These relations are no longer exact for interacting fermions [25].…”

mentioning

confidence: 99%

Extracting many-particle entanglement entropy from observables using supervised machine learning

Berkovits

2018

Phys. Rev. B

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Entanglement, which quantifies non-local correlations in quantum mechanics, is the fascinating concept behind much of aspiration towards quantum technologies. Nevertheless, directly measuring the entanglement of a many-particle system is very challenging. Here we show that via supervised machine learning using a convolutional neural network, we can infer the entanglement from a measurable observable for a disordered interacting quantum many-particle system. Several structures of neural networks were tested and a convolutional neural network akin to structures used for image and speech recognition performed the best. After training on a set of 500 realizations of disorder, the network was applied to 200 new realizations and its results for the entanglement entropy were compared to a direct computation of the entanglement entropy. Excellent agreement was found, except for several rare region which in a previous study were identified as belonging to an inclusion of a Griffiths-like quantum phase. Training the network on a test set with different parameters (in the same phase) also works quite well.

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Entanglement entropy and particle number cumulants of disordered fermions

Cited by 8 publications

References 32 publications

Many-body synchronization of interacting qubits by engineered ac-driving

Many-body synchronization of interacting qubits by engineered ac-driving

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

Extracting many-particle entanglement entropy from observables using supervised machine learning

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