Many-Body Entanglement: a New Application of the Full Counting Statistics

Klich, Israel; Levitov, L. S.; Лебедев, В. С.; Фейгельман, М. В.

doi:10.1063/1.3149497

Cited by 24 publications

(35 citation statements)

References 40 publications

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“…Some bounds relating S A to thermodynamic observables have been derived [142], but this is still far from being an operational measure. However, there is one recent interesting proposal to measure the entanglement entropy out of equilibrium, in the setup of the local quench we have just described [7,143,144]. The main idea of Klich and Levitov is to relate the entanglement between two half-chains to the distribution of the electrons passing towards the contact between them.…”

Section: Local Quench Quantum Noise and Measuring The Entanglementmentioning

confidence: 99%

Entanglement entropy and conformal field theory

Calabrese

Cardy

2009

J. Phys. A: Math. Theor.

1,590

100

2,187

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We review the conformal field theory approach to entanglement entropy in 1+1 dimensions. We show how to apply these methods to the calculation of the entanglement entropy of a single interval, and the generalization to different situations such as finite size, systems with boundaries, and the case of several disjoint intervals. We discuss the behaviour away from the critical point and the spectrum of the reduced density matrix. Quantum quenches, as paradigms of non-equilibrium situations, are also considered.

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Section: Local Quench Quantum Noise and Measuring The Entanglementmentioning

confidence: 99%

Entanglement entropy and conformal field theory

Calabrese

Cardy

2009

J. Phys. A: Math. Theor.

1,590

100

2,187

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“…Let us derive Eq. (28). The entanglement entropy (27) has the following cumulant expansion [27][28][29][30],…”

Section: Entanglement Entropymentioning

confidence: 99%

Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains

2020

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We consider an integrable system of two one-dimensional fermionic chains connected by a link. The hopping constant at the link can be different from that in the bulk. Starting from an initial state in which the left chain is populated while the right is empty, we present time-dependent full counting statistics and the Loschmidt echo in terms of Fredholm determinants. Using this exact representation, we compute the above quantities as well as the current through the link, the shot noise and the entanglement entropy in the large time limit. We find that the physics is strongly affected by the value of the hopping constant at the link. If it is smaller than the hopping constant in the bulk, then a local steady state is established at the link, while in the opposite case all physical quantities studied experience persistent oscillations. In the latter case the frequency of the oscillations is determined by the energy of the bound state and, for the Loschmidt echo, by the bias of chemical potentials.

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“…More recently, the connection of bipartite entanglement and measurement noise was explored as a way of quantifying entanglement entropy [7,61,62]. We define "measurement entropy" of an observableÔ, as the Shannon entropy S[Ô] = − x P (x) log P (x) associated with the probability distribution P (x) of the outcomes x ofÔ [63].…”

Section: Measurement Entropy and Bounds On Entanglement Entropymentioning

confidence: 99%

Criticality and entanglement in random quantum systems

Refael¹,

Moore²

2009

J. Phys. A: Math. Theor.

103

102

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Abstract. We review studies of entanglement entropy in systems with quenched randomness, concentrating on universal behavior at strongly random quantum critical points. The disorder-averaged entanglement entropy provides insight into the quantum criticality of these systems and an understanding of their relationship to non-random ("pure") quantum criticality. The entanglement near many such critical points in one dimension shows a logarithmic divergence in subsystem size, similar to that in the pure case but with a different universal coefficient. Such universal coefficients are examples of universal critical amplitudes in a random system. Possible measurements are reviewed along with the one-particle entanglement scaling at certain Anderson localization transitions. We also comment briefly on higher dimensions and challenges for the future.Criticality and entanglement in random quantum systems 2

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Many-Body Entanglement: a New Application of the Full Counting Statistics

Cited by 24 publications

References 40 publications

Entanglement entropy and conformal field theory

Entanglement entropy and conformal field theory

Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains

Criticality and entanglement in random quantum systems

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