Entanglement contour

Abstract

In the context of characterizing the structure of quantum entanglement in many-body systems, we introduce the entanglement contour, a tool to identify which real-space degrees of freedom contribute, and how much, to the entanglement of a region A with the rest of the system B. The entanglement contour provides a complementary, more refined approach to characterizing entanglement than just considering the entanglement entropy between A and B, with several concrete advantages. We illustrate this in the context of ground states and quantum quenches in fermionic quadratic systems. For instance, in a quantum critical system in $D=1$ spatial dimensions, the entanglement contour allows us to determine the central charge of the underlying conformal field theory from just a single partition of the system into regions A and B, (using the entanglement entropy for the same task requires considering several partitions). In $D\ge 2$ dimensions, the entanglement contour can distinguish between gapped and gapless phases that obey a same boundary law for entanglement entropy. During a local or global quantum quench, the time-dependent contour provides a detailed account of the dynamics of entanglement, including propagating entanglement waves, which offers a microscopic explanation of the behavior of the entanglement entropy as a function of time.

16 pages, 15 figures

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Cited by in corpus (67)

• Quantum quenches in 1+1 dimensional conformal field theories
• Fermionic Gaussian states: an introduction to numerical approaches
• Holographic entanglement contour, bit threads, and the entanglement tsunami
• Random matrices and entanglement entropy of trapped Fermi gases
• Entanglement Hamiltonians of lattice models via the Bisognano-Wichmann theorem
• Analytical results for the entanglement Hamiltonian of a free-fermion chain
• Area law and its violation: A microscopic inspection into the structure of entanglement and fluctuations
• Fine structure in holographic entanglement and entanglement contour
• Balanced Partial Entanglement and the Entanglement Wedge Cross Section
• Shaping contours of entanglement islands in BCFT
• Operator and entanglement growth in non-thermalizing systems: many-body localization and the random singlet phase
• Quantum vs. classical information: operator negativity as a probe of scrambling
• Towards the generalized gravitational entropy for spacetimes with non-Lorentz invariant duals
• Entanglement as geometry and flow
• Modular Hamiltonians for the massless Dirac field in the presence of a boundary
• Post measurement bipartite entanglement entropy in conformal field theories
• Modular Hamiltonians for the massless Dirac field in the presence of a defect
• Balanced Partial Entanglement and Mixed State Correlations
• Bit threads, Einstein's equations and bulk locality
• Entanglement contour perspective for strong area law violation in a disordered long-range hopping model
• The negativity contour: a quasi-local measure of entanglement for mixed states
• Entanglement entropy from entanglement contour: higher dimensions
• Formulas for Partial Entanglement Entropy
• Generalized mutual informations of quantum critical chains
• The PEE aspects of entanglement islands from bit threads
• Local measures of entanglement in black holes and CFTs
• Quantum Entanglement of Fermionic Local Operators
• Subsystem complexity after a global quantum quench
• Deriving the PEE proposal from the Locking bit thread configuration
• Covariant entanglement wedge cross-section, balanced partial entanglement and gravitational anomalies
• On the continuum limit of the entanglement Hamiltonian of a sphere for the free massless scalar field
• Ownerless island and partial entanglement entropy in island phases
• Quantum bit threads
• Modular conjugations in 2D conformal field theory and holographic bit threads
• Probing RG flows, symmetry resolution and quench dynamics through the capacity of entanglement
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• Link representation of the entanglement entropies for all bipartitions
• Piercing the rainbow: entanglement on an inhomogeneous spin chain with a defect
• Momentum-space entanglement after a quench in one-dimensional disordered fermionic systems
• Geometrizing the Partial Entanglement Entropy: from PEE Threads to Bit Threads
• Converting long-range entanglement into mixture: tensor-network approach to local equilibration
• Quantum bit threads and holographic entanglement
• Entanglement renormalization and integral geometry
• On the entanglement contour of excited states in the holographic CFT
• Phase transition and evidence of fast-scrambling phase in measurement-only quantum circuit
• Subsystem complexity after a local quantum quench
• More on the upper bound of holographic n-partite information
• Excited-Eigenstate Entanglement Properties of XX Spin Chains with Random Long-Range Interactions
• Holographic thermal entropy from geodesic bit threads
• Entanglement structures from modified IR geometry
• Topological Modes in Monitored Quantum Dynamics
• Entanglement Fractalization
• Local Information Flow in Quantum Quench Dynamics
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• Geometric entanglement in integer quantum Hall states with boundaries
• First Law and Quantum Correction for Holographic Entanglement Contour
• Weaving the (AdS) spaces with partial entanglement entropy threads
• Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States
• Bit Threads: From Entanglement to Geometric Entropies
• Hyperfine Structure of Quantum Entanglement
• Engineering large end-to-end correlations in finite fermionic chains
• Generation of Volume-Law Entanglement by Local-Measurement-Only Quantum Dynamics
• Holographic Tensor Networks as Tessellations of Geometry
• Rényi Entanglement of Purification and Half Rényi Reflected Entropy in Free Scalar Theory
• Bulk reconstruction of AdS${}_{d+1}$ metrics and developing kinematic space
• A contour for the entanglement negativity of bosonic Gaussian states
• Emergent geometry from entanglement structure