Holographic entanglement contour, bit threads, and the entanglement tsunami

Abstract

We study the entanglement contour, a quasi-local measure of entanglement, and propose a generic formula for the contour in 1+1d quantum systems. We use this formalism to investigate the real space entanglement structure of various static CFTs as well as local and global quantum quenches. The global quench elucidates the spatial distribution of entanglement entropy in strongly interacting CFTs and clarifies the interpretation of the entanglement tsunami picture. The entanglement tsunami effectively characterizes the non-local growth of entanglement entropy while the contour characterizes the local propagation of entanglement. We generalize the formula for the entanglement contour to arbitrary dimensions and entangling surface geometries using bit threads, and are able to realize a holographic contour for logarithmic negativity and the entanglement of purification by restricting the bulk spacetime to the entanglement wedge. Furthermore, we explore the connections between the entanglement contour, bit threads, and entanglement density in kinematic space.

7 pages, 4 figures; v2: typos corrected and references added to match published version in J. Phys. A

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Cited by in corpus (27)

• Balanced Partial Entanglement and the Entanglement Wedge Cross Section
• Shaping contours of entanglement islands in BCFT
• Balanced Partial Entanglement and Mixed State Correlations
• The PEE aspects of entanglement islands from bit threads
• Local measures of entanglement in black holes and CFTs
• Evolution of Entanglement Wedge Cross Section Following a Global Quench
• Deriving the PEE proposal from the Locking bit thread configuration
• Covariant entanglement wedge cross-section, balanced partial entanglement and gravitational anomalies
• 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
• Geometrizing the Partial Entanglement Entropy: from PEE Threads to Bit Threads
• Quantum bit threads and holographic entanglement
• Thread/State correspondence: from bit threads to qubit threads
• Holographic thermal entropy from geodesic bit threads
• Multipartite Optimized Correlation Measures and Holography
• Improved proof-by-contraction method and relative homologous entropy inequalities
• Entanglement structures from modified IR geometry
• Towards bit threads in general gravitational spacetimes
• Local Information Flow in Quantum Quench Dynamics
• First Law and Quantum Correction for Holographic Entanglement Contour
• Weaving the (AdS) spaces with partial entanglement entropy threads
• Phase Transitions of Correlations in Black Hole Geometries
• Holographic Tensor Networks as Tessellations of Geometry
• Emergent geometry from entanglement structure
• A contour for the entanglement negativity of bosonic Gaussian states