A universal entropy formula for topological tensor networks with continuous gauge groups is derived, comprising a differential entropy term, an area operator expectation, and a bulk entropy contribution.
Comments on Defining Entanglement Entropy
7 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We revisit the issue of defining the entropy of a spatial region in a broad class of quantum theories. In theories with explicit regularizations, working within an elementary but general algebraic framework applicable to matter and gauge theories alike, we give precise path integral expressions for three known types of entanglement entropy that we call full, distillable, and gauge-invariant. For a class of gauge theories that do not necessarily have a regularization in our framework, including Chern-Simons theory, we describe a related approach to defining entropies based on locally extending the Hilbert space at the entangling edge, and we discuss its connections to other calculational prescriptions. Based on results from both approaches, we conjecture that it is always the full entanglement entropy that is calculated by standard holographic techniques in strongly coupled conformal theories.
representative citing papers
The paper derives the exact one-loop de Sitter entropy for arbitrary higher-spin field content and all-loop results for 3D higher-spin gravity via a bulk-edge character formula.
Using full Gaussian purifications, the authors compute entanglement and complexity of purification in free boson and Ising CFTs, confirming universal EoP formulas and finding sub-polynomial decay of mutual information and EoP at large separations in the free boson.
For a two-dimensional corner symmetry algebra, coherent corner states give an entanglement entropy that scales with the area when mapped to near-extremal Reissner-Nordström black holes.
Minimal edge modes compatible with Chern-Simons topological invariance are proposed as quantum group particles, yielding a factorization of 3d gravity state space that matches proposals linking Bekenstein-Hawking entropy to topological entanglement entropy.
Generalizes channel-state duality to algebras with centers, establishing a link between state non-separability and channel isometry, plus extension to infinite-dimensional trace-class operators.
The continuum entropic c-function of the 2+1 dimensional Z2 gauge theory is reported to show a power-law short-distance regime and an exponential large-distance decay, with a crossover near l m_g = 1.
citing papers explorer
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Entanglement entropy in topological tensor networks
A universal entropy formula for topological tensor networks with continuous gauge groups is derived, comprising a differential entropy term, an area operator expectation, and a bulk entropy contribution.
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Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions
The paper derives the exact one-loop de Sitter entropy for arbitrary higher-spin field content and all-loop results for 3D higher-spin gravity via a bulk-edge character formula.
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Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories
Using full Gaussian purifications, the authors compute entanglement and complexity of purification in free boson and Ising CFTs, confirming universal EoP formulas and finding sub-polynomial decay of mutual information and EoP at large separations in the free boson.
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Entanglement Entropy of Quantum Corners
For a two-dimensional corner symmetry algebra, coherent corner states give an entanglement entropy that scales with the area when mapped to near-extremal Reissner-Nordström black holes.
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Minimal Factorization of Chern-Simons Theory -- Gravitational Anyonic Edge Modes
Minimal edge modes compatible with Chern-Simons topological invariance are proposed as quantum group particles, yielding a factorization of 3d gravity state space that matches proposals linking Bekenstein-Hawking entropy to topological entanglement entropy.
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Channel-State duality with centers
Generalizes channel-state duality to algebras with centers, establishing a link between state non-separability and channel isometry, plus extension to infinite-dimensional trace-class operators.
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Duality and entanglement in lattice gauge theories
The continuum entropic c-function of the 2+1 dimensional Z2 gauge theory is reported to show a power-law short-distance regime and an exponential large-distance decay, with a crossover near l m_g = 1.