Renyi entanglement entropies of descendant states in critical systems with boundaries: conformal field theory and spin chains

Year: 2016

Authors: Taddia L., Ortolani F., Palmai T.

Autors Affiliation: Scuola Normale Super Pisa, Piazza Cavalieri 7, I-56126 Pisa, Italy; CNR, Ist Nazl Ott, Sede Secondaria Sesto Fiorentino, Via Carrara 1, I-50019 Sesto Fiorentino, Italy; Univ Bologna, Dipartimento Fis & Astron, Via Irnerio 46, I-40127 Bologna, Italy; Ist Nazl Fis Nucl, Sez Bologna, Via Irnerio 46, I-40127 Bologna, Italy; Budapest Univ Technol & Econ, Inst Phys, MTA BME Lendulet Stat Field Theory Res Grp, Budafoki Ut 8, H-1111 Budapest, Hungary.

Abstract: We discuss the Renyi entanglement entropies of descendant states in critical one-dimensional systems with boundaries, that map to boundary conformal field theories in the scaling limit. We unify the previous conformal-field-theory approaches to describe primary and descendant states in systems with both open and closed boundaries. We provide universal expressions for the first two descendants in the identity family. We apply our technique to critical systems belonging to different universality classes with non-trivial boundary conditions that preserve conformal invariance, and find excellent agreement with numerical results obtained for finite spin chains. We also demonstrate that entanglement entropies are a powerful tool to resolve degeneracy of higher excited states in critical lattice models.

Journal/Review: JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT

Volume: 2016      Pages from: 93104-1  to: 93104-29

More Information: We thank G Sierra for important discussions, for stimulating our interest in the project and for a careful reading of the manuscript; we thank M I Berganza and G Takacs for valuable discussions. We acknowledge INFN-CNAF for providing computational resources and support, and D Cesini in particular; we thank S Sinigardi for technical support. LT acknowledges financial support from the EU integrated project SIQS, while TP from the Hungarian Academy of Sciences through grant No. LP2012-50 and a postdoctoral fellowship.
KeyWords: conformal field theory; density matrix renormalisation group; entanglement in extended quantum systems; spin chains; ladders and planes
DOI: 10.1088/1742-5468/2016/09/093104

Citations: 24
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