Excited state entanglement in one dimensional quantum critical systems: Extensivity and the role of microscopic details

Abstract

We study entanglement via the subsystem purity relative to bipartitions of arbitrary excited states in (1+1)-dimensional conformal field theory, equivalent to the scaling limit of one dimensional quantum critical systems. We compute the exact subpurity as a function of the relative subsystem size for numerous excited states in the Ising and three-state Potts models. We find that it decays exponentially when the system and the subsystem sizes are comparable until a saturation limit is reached near half-partitioning, signaling that excited states are maximally entangled. The exponential behavior translates into extensivity for the second Rényi entropy. Since the coefficient of this linear law depends only on the excitation energy, this result shows an interesting, new relationship between energy and quantum information and elucidates the role of microscopic details.

4.5 pages, 2 figures. v2: results unchanged but the text is completely rewritten and many aspects are clarified. Version accepted to PRB as Rapid Communication

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Cited by in corpus (9)

• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
• Quantum Entanglement of Localized Excited States at Finite Temperature
• Entanglement entropy and negativity of disjoint intervals in CFT: Some numerical extrapolations
• Entanglement Entropy Scaling Laws and Eigenstate Typicality in Free Fermion Systems
• Bound states and entanglement in the excited states of quantum spin chains
• Relative Entanglement Entropies in 1+1-dimensional conformal field theories
• Entanglement Entropy from the Truncated Conformal Space
• Quantum dimensions from local operator excitations in the Ising model