Generalized entanglement entropies in two-dimensional conformal field theory

Understand

We introduce and study generalized R\'enyi entropies defined through the traces of products of ${\rm Tr}_B (|\Psi_i\rangle\langle \Psi_j|)$ where $|\Psi_i\rangle$ are eigenstates of a two-dimensional conformal field theory (CFT).

• When $|\Psi_i\rangle=|\Psi_j\rangle$ these objects reduce to the standard R\'enyi entropies of the eigenstates of the CFT.
• Exploiting the path integral formalism, we show that the second generalized R\'enyi entropies are equivalent to four-point correlators.
• We then focus on a free bosonic theory for which the mode expansion of the fields allows us to develop an efficient strategy to compute the second generalized R\'enyi entropy for all eigenstates.