Area law and its violation: A microscopic inspection into the structure of entanglement and fluctuations

Abstract

Quantum fluctuations of local quantities can be a direct signature of entanglement in an extended quantum many-body system. Hence they may serve as a theoretical (as well as an experimental) tool to detect the spatial properties of the entanglement entropy of a subsystem. In the ground state of quantum many-body systems, its scaling is typically linear in the boundary of the subsystem (area law). Here we propose a microscopic insight into the spatial structure of entanglement and fluctuations using the concept of \emph{contour}, recently introduced to decompose the bipartite entanglement entropy of lattice free fermions between two extended regions $A$ and $B$ into contributions from single sites in $A$. We generalize the notion of contour to the entanglement of any quadratic (bosonic or fermionic) lattice Hamiltonian, as well as to particle-number fluctuations. The entanglement and fluctuations contours are found to generally decay when moving away from the boundary between $A$ and $B$. We show that in the case of free fermions the decay of the entanglement contour follows closely that of the fluctuation contour. In the case of Bose-condensed interacting bosons, treated via the Bogoliubov and spin-wave approximations, such a link cannot be established -- fluctuation and entanglement contours are found to be radically different, as they lead to a logarithmically violated area law for fluctuations, and to a strict area law of entanglement. Analyzing in depth the role of the zero-energy Goldstone mode of spin-wave theory, and of the corresponding lowest-energy mode in the entanglement spectrum, we unveil a subtle interplay between the special contour and energy scaling of the latter, and universal additive logarithmic corrections to entanglement area law discussed extensively in the recent literature.

24 pages, 14 figures

References in corpus (15)

• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Universal terms for the entanglement entropy in 2+1 dimensions
• Spatial structures and localization of vacuum entanglement in the linear harmonic chain
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• Entanglement Entropy of the Two-Dimensional Heisenberg Antiferromagnet
• Interpretation of scanning tunneling quasiparticle interference and impurity states in cuprates
• Entanglement entropy scaling in the bilayer Heisenberg spin system
• Corner contribution to the entanglement entropy of strongly-interacting O(2) quantum critical systems in 2+1 dimensions
• Entanglement Energetics at Zero Temperature
• Detecting Goldstone Modes with Entanglement Entropy
• Entanglement Entropy and Mutual Information in Bose-Einstein Condensates
• Universal logarithmic corrections to entanglement entropies in two dimensions with spontaneously broken continuous symmetries
• Area Law for Gapless States from Local Entanglement Thermodynamics
• The scaling of entanglement entropy in a honeycomb lattice on a torus
• Structure of entanglement in regulated Lorentz invariant field theories

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• Probing RG flows, symmetry resolution and quench dynamics through the capacity of entanglement
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• Gaussian-state Ansatz for the non-equilibrium dynamics of quantum spin lattices
• Entanglement properties and ground-state statistics of free bosons
• Single-shot holographic compression from the area law
• Bipartite Fluctuations of Critical Fermi Surfaces
• Emergent universality in critical quantum spin chains: entanglement Virasoro algebra
• Spin-wave study of entanglement and Rényi entropy for coplanar and collinear magnetic orders in two-dimensional quantum Heisenberg antiferromagnets
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• Evolution of entanglement entropy in strongly correlated bosons in an optical lattice
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• Rényi entanglement entropy after a quantum quench starting from insulating states in a free boson system
• Entanglement entropy in low-energy field theories at finite chemical potential
• Hyperfine Structure of Quantum Entanglement
• Dynamics of entanglement asymmetry for space-inversion symmetry of free fermions on honeycomb lattices
• A contour for the entanglement negativity of bosonic Gaussian states
• Probing non-Gaussian correlations through entanglement generation in a many-body quantum system
• Entanglement entropy dynamics of non-Gaussian states in free boson systems: Random sampling approach
• Emergent geometry from entanglement structure