The past 20 years have solidified quantum entanglement as a research topic of continued and central interest for physicists working in domains as diverse as high energy physics, condensed matter theory and quantum information. Most relevantly for this talk, entanglement measures have turned out to be a powerful probe into the physics of 1D quantum critical systems.
Most known results for such setups address the entanglement in critical quantum systems with periodic BC. For open systems, there are results for the Rényi entropies and other entanglement measures of an interval touching one of the boundaries with the rest of the system. However, for more generic bipartitions or mixed boundaries, few exact calculations have been completed.
In this talk, I will show how the second Rényi entropy of an interval disconnected from the boundary can be computed exactly, through CFT methods, provided the same conformal boundary condition is applied on both sides. This will be followed by a comparison with spin chain numerics and a discussion of finite-size effects.
Finally, I will also succinctly present some results for Rényi entropies in systems with mixed boundaries.
 M. Fagotti, Phys. Rev. Lett. 128, 110602 (2022) [arXiv:2110.11322]
 M. Fagotti, V. Marić, and L. Zadnik, arXiv:2205.02221.
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