Entanglement spectrum degeneracy and the Cardy formula in 1+1 dimensional conformal field theories. (11th December 2017)

• Record Type: Journal Article
• Authors: Alba, Vincenzo; Calabrese, Pasquale; Tonni, Erik
• Is Part Of: Journal of physics. Volume 51:Number 2(2018)
• Publication Date: 2017-12-11
• Subjects: Cardy formula -- entanglement spectrum -- spin chains -- conformal field theory -- integrability -- negativity spectrum; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa9365
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We investigate the effect of a global degeneracy in the distribution of the entanglement spectrum in conformal field theories in one spatial dimension. We relate the recently found universal expression for the entanglement Hamiltonian to the distribution of the entanglement spectrum. The main tool to establish this connection is the Cardy formula. It turns out that the Affleck–Ludwig non-integer degeneracy, appearing because of the boundary conditions induced at the entangling surface, can be directly read from the entanglement spectrum distribution. We also clarify the effect of the non-integer degeneracy on the spectrum of the partial transpose, which is the central object for quantifying the entanglement in mixed states. We show that the exact knowledge of the entanglement spectrum in some integrable spin-chains provides strong analytical evidences corroborating our results.