Generalized entanglement entropies in two-dimensional conformal field theory

Abstract

We introduce and study generalized Rényi entropies defined through the traces of products of ${\mathrm{Tr}}_B(|{\Psi }_i⟩⟨{\Psi }_j|)$ where $|{\Psi }_i⟩$ are eigenstates of a two-dimensional conformal field theory (CFT). When $|{\Psi }_i⟩=|{\Psi }_j⟩$ these objects reduce to the standard Rényi entropies of the eigenstates of the CFT. Exploiting the path integral formalism, we show that the second generalized Rényi entropies are equivalent to four-point correlators. We then focus on a free bosonic theory for which the mode expansion of the fields allows us to develop an efficient strategy to compute the second generalized Rényi entropy for all eigenstates. As a byproduct, our approach also leads to new results for the standard Rényi and relative entropies involving arbitrary descendent states of the bosonic CFT.

29 pages, 4 figures, published version

References in corpus (21)

• Entanglement negativity in quantum field theory
• Entanglement entropy of two disjoint intervals in conformal field theory II
• Relative entropy and the Bekenstein bound
• Entanglement of low-energy excitations in Conformal Field Theory
• Entanglement entropy of two disjoint blocks in XY chains
• The g-theorem and quantum information theory
• Relative Entropies in Conformal Field Theory
• Local temperatures and local terms in modular Hamiltonians
• Symmetry resolved relative entropies and distances in conformal field theory
• Pseudo Entropy in Free Quantum Field Theories
• Symmetry decomposition of relative entropies in conformal field theory
• Subsystem Trace Distance in Quantum Field Theory
• Relative entropy of excited states in conformal field theories of arbitrary dimensions
• Shell-Filling Effect in the Entanglement Entropies of Spinful Fermions
• Excited state entanglement in one dimensional quantum critical systems: Extensivity and the role of microscopic details
• Relative Entanglement Entropies in 1+1-dimensional conformal field theories
• Thermality and excited state Rényi entropy in two-dimensional CFT
• Entanglement Entropies of the quarter filled Hubbard model
• Entanglement of magnon excitations in spin chains
• Subsystem distance after a local operator quench
• Entanglement Entropy from the Truncated Conformal Space

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• On symmetry-resolved generalized entropies