Entanglement spectrum degeneracy and the Cardy formula in 1+1 dimensional conformal field theories

2017/07/24 by Vincenzo Alba, Pasquale Calabrese, Erik Tonni · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Boundary conformal field theory #Boundary value problem #Conformal field theory #Conformal map #Degeneracy (biology) #Hamiltonian (control theory) #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Squashed entanglement #Theoretical physics #cond-mat.stat-mech #hep-th

paper · pdf · doi:10.1088/1751-8121/aa9365

published as J. Phys. A 51 024001 (2018) · 24 pages, 3 figures

arxiv created 2017/07/24 · openalex created_date 2017/07/31 · openalex publication_date 2017/10/13 · arxiv updated 2017/12/14 · openalex updated_date 2026/08/05

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.

Citations

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Cited by

• Subsystem complexity after a local quantum quench
• A new look at the entanglement entropy of a single interval in a 2d CFT
• On entanglement Hamiltonians of an interval in massless harmonic chains