R\'enyi entropies for one-dimensional quantum systems with mixed boundary conditions

Understand

We present a general method for calculating R\'enyi entropies in the ground state of a one-dimensional critical system with mixed open boundaries, for an interval starting at one of its ends.

• In the conformal field theory framework, this computation boils down to the evaluation of the correlation function of one twist field and two boundary condition changing operators in the cyclic orbifold.
• Exploiting null-vectors of the cyclic orbifold, we derive ordinary differential equations satisfied by these correlation functions.
• In particular, we obtain an explicit expression for the second R\'enyi entropy valid for any diagonal minimal model, but with a particular set of mixed boundary conditions.