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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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
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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.
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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.
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.
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
Numerical MPS study of the Moore-Read state finds approximate equipartition of symmetry-resolved entanglement entropy and good agreement with the Li-Haldane conjecture for the entanglement spectrum despite distinct neutral and charged velocities.
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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Lecture notes surveying entanglement entropy in QFT and holography, emphasizing physical aspects and the Ryu-Takayanagi formula.
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