Entanglement hamiltonians in two-dimensional conformal field theory

Abstract

We enumerate the cases in 2d conformal field theory where the logarithm of the reduced density matrix (the entanglement or modular hamiltonian) may be written as an integral over the energy-momentum tensor times a local weight. These include known examples and new ones corresponding to the time-dependent scenarios of a global and local quench. In these latter cases the entanglement hamiltonian depends on the momentum density as well as the energy density. In all cases the entanglement spectrum is that of the appropriate boundary CFT. We emphasize the role of boundary conditions at the entangling surface and the appearance of boundary entropies as universal O(1) terms in the entanglement entropy.

30 pages, 10 figures

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Cited by in corpus (22)

• Entanglement in indistinguishable particle systems
• Local temperatures and local terms in modular Hamiltonians
• Defect extremal surface as the holographic counterpart of Island formula
• Irreversibility in quantum field theories with boundaries
• Relative Entanglement Entropies in 1+1-dimensional conformal field theories
• Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis
• Modular Hamiltonians for the massless Dirac field in the presence of a boundary
• Modular Hamiltonians for the massless Dirac field in the presence of a defect
• Anisotropic Unruh temperatures
• Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains
• Modular Hamiltonian of a chiral fermion on the torus
• Disentangling critical quantum spin chains with Clifford circuits
• Rényi entropy and negativity for massless complex boson at conformal interfaces and junctions
• Critical Scaling Behaviors of Entanglement Spectra
• Subsystem complexity after a local quantum quench
• Entanglement Entropy and Modular Hamiltonian of free fermion with deformations on a torus
• Boundary Symmetry Breaking in CFT and the String Order Parameter
• Entanglement Hamiltonian of Interacting Systems: Local Temperature Approximation and Beyond
• Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models
• Topological physics in quantum critical systems
• Negative R$\acute{\text{e}}$nyi entropy and Brane intersection
• Light-cone cuts and hole-ography: explicit reconstruction of bulk metrics