Subarea Law of Entanglement in Nodal Fermionic Systems

The classification of electron systems according to their topology has been at the forefront of condensed matter research in recent years. It has been found that systems of the same symmetry, previously thought of as equivalent, may in fact be distinguished by their topological properties. Moreover, the non-trivial topology found in some insulators and superconductors has profound physical implications that can be observed experimentally and can potentially be used for applications. However, characterizing a system's topology is not always a simple task, even for a theoretical model. When translation and other symmetries are present in a quadratic model the topological invariants are readily defined and easily calculated in a variety of symmetry classes. However, once interactions or disorder come into play the task becomes difficult, and in many cases prohibitively so. The goal of this paper is to test whether the entanglement entropy and entanglement spectrum bare signatures of the system's topology. Using quadratic models of superconductors we demonstrate that these entanglement properties are sensitive to changes in topology. arXiv:1407.5980v2 [cond-mat.str-el]

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“…As the sub-leading nature of these corrections makes it very hard to see them directly in the entanglement entropy, we look at the quantity 14 .…”

Section: Functional Dependence Of the Entanglement Entropymentioning

confidence: 99%

Entanglement spectrum as a probe for the topology of a spin-orbit-coupled superconductor

et al. 2014

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“…[3]). For a system with short-ranged interactions in d spatial dimensions, the area law states that the entanglement entropy of a region A of linear size L grows like L d−1 , that is like the area |∂A| of the boundary ∂A of A. Fermi liquids are extremely interesting from an entanglement perspective because they possesses long-range entanglement that manifests as a violation of the area law [4][5][6][7][8][9][10][11][12]. Indeed, entanglement entropy in a Fermi liquid ground state scales like L d−1 ln (L) hence showing a logarithmic violation of the area law.…”

Section: Introductionmentioning

confidence: 99%

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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“…The logarithm of the asymptotic behavior is related to the logarithmic area-law violation in lattice free fermions [10][11][12][13][14][15][16]. In homogeneous systems with periodic and open (hard-wall) boundary conditions (PBC and OBC respectively) the prefactor can be analytically computed [9] using the Widom conjecture [17].…”

mentioning

confidence: 99%

“…[27], the particle fluctuations and entanglement entropies can be computed using Eqs. (14)(15)(16)(17)(18)(19)(20)(21). In particular, for the particle variance we obtain…”

mentioning

confidence: 99%

Exact relations between particle fluctuations and entanglement in Fermi gases

Calabrese¹,

Mintchev²,

Vicari³

2012

EPL

123

182

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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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Subarea Law of Entanglement in Nodal Fermionic Systems

Cited by 29 publications

References 21 publications

Entanglement spectrum as a probe for the topology of a spin-orbit-coupled superconductor

Entanglement spectrum as a probe for the topology of a spin-orbit-coupled superconductor

Oscillating terms in the Renyi entropy of Fermi gases and liquids

Exact relations between particle fluctuations and entanglement in Fermi gases

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