Abstract
The Rényi-Shannon entropy allows extraction of some universal information about many-body wave functions. For a critical spin chain with central charge , we show that it exhibits a phase transition at some value of the Rényi parameter which depends on the Luttinger parameter . A replica-free formulation establishes a connection to boundary entropies in conformal field theory and reveals that the transition is triggered by a vertex operator which becomes relevant at the boundary. Our numerical results (XXZ and spin chains) match the continuum limit prediction, confirming its universal character. The replica approach used in previous works turns out to be correct only for . From the point of view of two-dimensional Rokhsar-Kivelson states, this transition reveals a singularity in the entanglement spectra.
- Received 26 October 2011
DOI:https://doi.org/10.1103/PhysRevB.84.195128
©2011 American Physical Society