Colloquium: Area laws for the entanglement entropy

By Jens Eisert, M. Cramer, Martin Bodo Plenio. 2010

1,286 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/73040f2096d90a62fa3c402a13324fd531c34e12

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Quantum thermalization through entanglement in an isolated many-body system (2016, background): “Ground-breaking theoretical work using conformal field theory has shown that indeed, at long times, a volume law is expected for a quenched, infinite, continuous system, while only an area law with a log correction is expected for the ground state [2, 33, 34].”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives (2017, methodology): “The entanglement spectra are determined by the eigenvalues of the reduced density matrix [Eisert et al., 2010, Zwanziger, 1994].”
Entanglement transition from variable-strength weak measurements (2019, methodology): “Alternative entanglement measures used in the literature include Rényi entropies [18, 20, 21] and mutual information [20, 21, 38].”
Entanglement Entropy of Black Holes (2011, background): “A number of very nice reviews appeared in recent years that address the role of entanglement entropy for black holes [21, 90, 146, 54]; review the calculation of entanglement entropy in quantum field theory in flat spacetime [81, 37] and the role of the conformal symmetry [31]; and focus on the holo”
Unsupervised Generative Modeling Using Matrix Product States (2017, background): “The success of TN description can be theoretically justified from a quantum information perspective [19, 20].”
The Physics of Communicability in Complex Networks (2011, methodology): “…theory, where it has been used, for example, to establish area laws for the entanglement entropy; see, e.g., (Cramer and Eisert, 2006; Cramer et al., 2006; Hastings, 2004; Hastings and Koma, 2006; Schuch, 2007; Schuch et al., 2006) and especially (Eisert et al., 2010) for a comprehensive survey.”
Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1 + 1d (2016, background): “In particular, the simulability of ground states of local Hamiltonians is intimately related (see [9, 10] for precise statements) to the area law [11]: for gapped Hamiltonians, the entanglement entropy of a subsystem A is bounded [12], while for gapless systems, the area law is only weakly violated—”
Decay properties for functions of matrices over $C^*$-algebras (2013, neutral): “Such properties play an important role in various applications including electronic structure computations in quantum chemistry [3, 10], quantum information theory [14, 15, 24, 48], high-dimensional statistics [1], random matrix theory [43] and numerical analysis [9, 53], to name a few.”
Entanglement certification from theory to experiment (2018, background): “of high importance in the field of condensed matter physics [33, 35].”
Complexity and entanglement for thermofield double states (2018, background): “(332) and (342), the covariance matrix of the initial vacuum state is found to be G = diag δ1/2 x−1/2,δ−1/2 x1/2,δ1/2 x−1/2,δ−1/2 x1/2 (343) in terms of the matrix square root of x and its inverse [87].”
Random Quantum Circuits (2022, background): “Second, just as patterns of entanglement in equilibrium matter contain universal structures that are characteristic of phases and phase transitions (43, 19, 44, 45), entanglement is also an organizing principle for out-ofequilibrium quantum matter.”
Hand-waving and interpretive dance: an introductory course on tensor networks (2016, background): “If we consider the case of local and gapped Hamiltonians, it has been shown that the relevant ground states cannot be highly entangled [19, 37–40] (see [41] for a review).”
Colloquium : Many-body localization, thermalization, and entanglement (2018, background): “Area-law entanglement scaling is typical of ground states in gapped systems (Eisert et al., 2010; Verstraete et al., 2008).”
Lattice gauge theory simulations in the quantum information era (2016, background): “In this context, possible implementations of spin IceHamiltonians have been proposed using different platforms, both analogue and digital ones.”