The entanglement entropy of one-dimensional systems in continuous and homogeneous space

Calabrese, Pasquale; Mintchev, Mihail; Vicari, Ettore

doi:10.1088/1742-5468/2011/09/p09028

Cited by 83 publications

(139 citation statements)

References 77 publications

(190 reference statements)

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“…[20] and elsewhere, there are also subleading oscillating terms in the Renyi entropy. Similar oscillations have been extensively studied in one dimension [25][26][27][28][29][30][31]. Here we compute these subleading oscillating terms in the Renyi entropy analytically for the free Fermi gas in higher dimensions.…”

Section: Introductionsupporting

confidence: 57%

Oscillating terms in the Renyi entropy of Fermi gases and liquids

Swingle

McMinis

Tubman³

2013

Phys. Rev. B

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In this work we compute subleading oscillating terms in the Renyi entropy of Fermi gases and liquids corresponding to 2kF -like oscillations. Our theoretical tools are the one dimensional formulation of Fermi liquid entanglement familiar from discussions of the logarithmic violation of the area law and quantum Monte Carlo calculations. The main result is a formula for the oscillating term for any region geometry and a spherical Fermi surface in any dimension. Specializing to two dimensions, we compare this term to numerical calculations of Renyi entropies using the correlation function method and find excellent agreement. We also compare with quantum Monte Carlo data on interacting Fermi liquids where we also find agreement up to moderate interaction strengths.

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Section: Introductionsupporting

confidence: 57%

Oscillating terms in the Renyi entropy of Fermi gases and liquids

Swingle

McMinis

Tubman³

2013

Phys. Rev. B

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“…If one is able to calculate (the asymptotic behaviour of) D A (λ), the entanglement entropies are given by Eq. (7) as the integral [75,79] …”

Section: Entanglement Entropies and Particle Fluctuationsmentioning

confidence: 99%

Stationary entanglement entropies following an interaction quench in 1D Bose gas

Collura¹,

Kormos²,

Calabrese³

2014

J. Stat. Mech.

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We analyze the entanglement properties of the asymptotic steady state after a quench from free to hard-core bosons in one dimension. The Rényi and von Neumann entanglement entropies are found to be extensive, and the latter coincides with the thermodynamic entropy of the Generalized Gibbs Ensemble (GGE). Computing the spectrum of the twopoint function, we provide exact analytical results both for the leading extensive parts and the subleading terms for the entropies as well as for the cumulants of the particle number fluctuations. We also compare the extensive part of the entanglement entropy with the thermodynamic ones, showing that the GGE entropy equal the entanglement one and it is the double of the diagonal entropy.

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“…The possibility of turning these expansions into an effective measure of entanglement depends on its convergence properties, which appear problematic due to the behavior of the coefficients s (α) k with increasing k. In this paper we investigate the relations between entanglement entropies and particle fluctuations, and in particular the convergence properties of the formal expansions (5)(6)(7)(8). We will show that, in noninteracting fermion gases with N particles in a finite volume of any dimension d, the expansion (5) gets effectively truncated in the large-N limit, because the high cumulants V (n) A with n > 2 are all suppressed relatively to the particle variance…”

mentioning

confidence: 99%

“…The many-body ground state is obtained by filling the lowest N one-particle energy levels φ n (x). The cumulants V (m) A of the particle-number distribution and the entanglement entropies of a subsystem A can be written in terms of the overlap matrix [7,8] …”

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confidence: 99%

Exact relations between particle fluctuations and entanglement in Fermi gases

Calabrese¹,

Mintchev²,

Vicari³

2012

EPL

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We derive exact relations between the Rényi entanglement entropies and the particle number fluctuations of (connected and disjoint) spatial regions in systems of N noninteracting fermions in arbitrary dimension. We prove that the asymptotic large-N behavior of the entanglement entropies is proportional to the variance of the particle number. We also consider 1D Fermi gases with a localized impurity, where all particle cumulants contribute to the asymptotic large-N behavior of the entanglement entropies. The particle cumulant expansion turns out to be convergent for all integer-order Rényi entropies (except for the von Neumann entropy) and the first few cumulants provide already a good approximation. Since the particle cumulants are accessible to experiments, these relations may provide a measure of entanglement in these systems. The nature of the quantum correlations of manybody systems, and in particular the entanglement phenomenon, are fundamental physical issues. They have attracted much theoretical interest in the last few decades, due to the impressive progress in the experimental activity in atomic physics, quantum optics and nanoscience, which has provided a great opportunity to investigate the interplay between quantum and statistical behaviors in particle systems. The great ability in the manipulation of cold atoms in optical lattice (see, e.g., Ref.[1]) has allowed the realization of physical systems which are accurately described by theoretical models such as Hubbard and Bose-Hubbard models in different dimensions, achieving through experimental checks of the fundamental theoretical paradigma of condensed matter physics.The quantum correlations arising in the ground state of quantum many-body systems can be characterized by the expectation values of the products of local operators, such as the particle density and one-particle operators, or by their integral over a space region A, such as the particle-number correlators within A,where n(x) is the particle-density operator andcounts the number of particles in A. Quantum correlations are also characterized by the fundamental phenomenon of entanglement, which gives rise to nontrivial connections between different parts of extended quantum systems [2]. A widely accepted measure of entanglement is given by the Rényi entropies of the reduced density matrix ρ A of a subsystem A:whose limit α → 1 provides the von Neumann (vN) entropy. Local correlations and bipartite entanglement entropies provide important and complementary information of the quantum features of many-body systems, of their ground states and of their unitary evolutions, because they probe different features of the quantum dynamics. However, the entanglement entropy is a highly nonlocal quantity which is difficult to measure. Designing an experimental protocol for its measurement represents a major challenge. A recent interesting proposal considers the particle fluctuations as effective probes of many-body entanglement [3][4][5][6]. This is based on the result that, for noninteracting fermions...

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The entanglement entropy of one-dimensional systems in continuous and homogeneous space

Cited by 83 publications

References 77 publications

Oscillating terms in the Renyi entropy of Fermi gases and liquids

Oscillating terms in the Renyi entropy of Fermi gases and liquids

Stationary entanglement entropies following an interaction quench in 1D Bose gas

Exact relations between particle fluctuations and entanglement in Fermi gases

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