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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Calabrese and J.L
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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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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.
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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.
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In f(R) theories, the replica-method gravitational entropy computed on the apparent horizon matches the Hollands-Wald-Zhang dynamical black hole entropy and satisfies the first law, while the event horizon does not; this lets the generalized second law be reinterpreted as matter entanglement across
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An operator-algebraic definition of timelike entanglement entropy in QFT is shown to be real-valued via the timelike tube theorem.
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