Proves integer Rényi QNEC by establishing log-convexity of Kosaki L^n norms under null-translation semigroups for σ-finite von Neumann algebras with half-sided modular inclusions, assuming only finite sandwiched Rényi divergence to the vacuum.
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Entanglement Entropy and Quantum Field Theory
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abstract
We carry out a systematic study of entanglement entropy in relativistic quantum field theory. This is defined as the von Neumann entropy S_A=-Tr rho_A log rho_A corresponding to the reduced density matrix rho_A of a subsystem A. For the case of a 1+1-dimensional critical system, whose continuum limit is a conformal field theory with central charge c, we re-derive the result S_A\sim(c/3) log(l) of Holzhey et al. when A is a finite interval of length l in an infinite system, and extend it to many other cases: finite systems,finite temperatures, and when A consists of an arbitrary number of disjoint intervals. For such a system away from its critical point, when the correlation length \xi is large but finite, we show that S_A\sim{\cal A}(c/6)\log\xi, where \cal A is the number of boundary points of A. These results are verified for a free massive field theory, which is also used to confirm a scaling ansatz for the case of finite-size off-critical systems, and for integrable lattice models, such as the Ising and XXZ models, which are solvable by corner transfer matrix methods. Finally the free-field results are extended to higher dimensions, and used to motivate a scaling form for the singular part of the entanglement entropy near a quantum phase transition.
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Replica wormholes in the gravitational path integral yield the island rule for the fine-grained entropy of Hawking radiation, ensuring it follows the unitary Page curve in two-dimensional dilaton gravity.
A hierarchy of approximations to the mutual information in CFTs is derived from modular flow and two-point functions of primaries, providing a high-precision formula for arbitrary ball separations that supersedes previous long-distance expansions.
In large-central-charge holographic CFTs, post-quench mutual information organizes into six phases governed by conformal block dominance and D4 symmetry breaking to Z2 x Z2.
Generalized entanglement entropies are constructed via left-, right-, and bi-invariant unit-invariant singular value decompositions to ensure scale invariance for non-Hermitian and rectangular operators in quantum mechanics, random matrices, and Chern-Simons theory.
An improved heat kernel framework with phase-factor reconstruction computes symmetry-resolved entanglement entropy for charged systems and derives a cMERA flow equation that agrees with CFT and holographic calculations.
MERA tensor networks produce continuously varying effective scaling dimensions along the Z3 chiral clock critical line, starting from 3-state Potts values as the chiral parameter increases.
A neutral current protocol on the lattice in the massive Thirring model yields a weak signal exactly matching a coarse-grained current correlator, with extracted energy scaling quadratically with measurement strength, identifying the neutral sector shared with the continuum.
Imaginary pseudo entropy provides a measurable, reversible record of temporal orientation in quantum transitions via replica interferometry and decreases under quantum channels per Petz recovery.
Proposes an exact kinematic sector in AdS/CFT using Weyl-frame CFT on open solid torus, treating AdS as kinematic geometry recovered only in singular limits, with two-point functions defining entanglement entropy without replicas.
Entangling power in Heisenberg spin chains shows a monotonic decrease with growing symmetry in small models, sharp dips at SU(2) and free-fermion points in finite chains, and vanishes at SU(2) points but maximizes at the free-fermion point in the thermodynamic limit for the S-matrix.
Uniform MPS simulations of dense 1+1D SU(2) gauge theory find Tomonaga-Luttinger liquid infrared behavior with central charge 1, density modulations at the predicted wavenumber, and a smooth crossover in the Luttinger parameter from K~1 to K~1/2 that realizes the quarkyonic picture with coexisting q
Quantum systems reach a Maximal Entanglement Limit where entanglement geometry produces thermal reduced density matrices and probabilistic behavior in statistical and high-energy physics.
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
Authors derive genuine multientropy for Lifshitz states as mutual information plus negativity, obtain its non-integer Rényi continuation, and prove dihedral invariants equal Rényi reflected entropies for general tripartite pure states.
Proves exact separability for disconnected subsystems in dimer RK states and exponentially suppressed entanglement for RVB states on arbitrary lattices, with negativity expressed via partition functions.
Replica analysis shows QNEC saturation in interacting CFTs with twist gap because only the stress-tensor defect operator produces the contact term in the n to 1 limit.
A variational quantum SVD framework with classical orthogonality correction enables high-precision extraction of Schmidt components from bipartite states using shallow circuits and classical tensor-network post-processing.
Fuzzball models with stretched horizons modify or eliminate entanglement islands depending on boundary conditions and cap geometry, producing information paradox analogues in some cases.
Holographic Schwinger pair creation generates nonlocal magic for spacetime dimensions d>2, as shown by a non-flat entanglement spectrum that can be read from the probe brane free energy.
At large central charge, BCFT von Neumann entropy with deformed boundaries is reproduced by island entropy in an emergent JT gravity setup with transparent boundary conditions set by the deformation.
Pseudo entropy distinguishes topological from trivial phases in the SSH model via sign of averaged excess entropy ΔS12 and tracks quench critical times with its imaginary part.
Modular quantization of a single holographic CFT reproduces exact Hartle-Hawking correlators of smooth BTZ black holes in the semiclassical limit while yielding non-smooth stretched-horizon descriptions at finite GN.
Review of integrable anyonic chains with new examples identified for su(2)_k, Tambara-Yamagami TY(Z_n), Fib x Fib, Fib x Ising, and preliminary results for Haagerup-Izumi categories.
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Replica Wormholes and the Entropy of Hawking Radiation
Replica wormholes in the gravitational path integral yield the island rule for the fine-grained entropy of Hawking radiation, ensuring it follows the unitary Page curve in two-dimensional dilaton gravity.
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Entropy Variations and Light Ray Operators from Replica Defects
Replica analysis shows QNEC saturation in interacting CFTs with twist gap because only the stress-tensor defect operator produces the contact term in the n to 1 limit.
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Lectures on entanglement entropy in field theory and holography
Lecture notes surveying entanglement entropy in QFT and holography, emphasizing physical aspects and the Ryu-Takayanagi formula.