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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.
We reconsider the moments of the reduced density matrix of two disjoint intervals and of its partial transpose with respect to one interval for critical free fermionic lattice models. It is known that these matrices are sums of either two or four Gau
The lectures provide a pedagogical introduction to the methods of CFT as applied to two-dimensional critical behaviour.
We review the imaginary time path integral approach to the quench dynamics of conformal field theories. We show how this technique can be applied to the determination of the time dependence of correlation functions and entanglement entropy for both g
We consider a quantum quench in a finite system of length $L$ described by a 1+1-dimensional CFT, of central charge $c$, from a state with finite energy density corresponding to an inverse temperature $betall L$. For times $t$ such that $ell/2<t<(L-e
We study the logarithmic negativity and the moments of the partial transpose in the ground state of a two dimensional massless harmonic square lattice with nearest neighbour interactions for various configurations of adjacent domains. At leading orde