Notes on Quantum Entanglement of Local Operators

Abstract

This is an expanded version of the short report arXiv:1401.0539, where we stud- ied the (Renyi) entanglement entropies for the excited state defined by acting a given local operator on the ground state. We introduced the (Renyi) entanglement entropies of given local operators which measure the degrees of freedom of local operators and characterize them in conformal field theories from the viewpoint of quantum entanglement. In present paper, we explain how to compute them in free massless scalar field theories and we also investigate their time evolution. The results are interpreted in terms of relativistic propagation of an entangled pair. The main new results which we acquire in the present paper are as follows. Firstly, we provide an explanation which shows that the (Renyi) entanglement entropies of a specific operator are given by (Renyi) entanglement entropies of binomial distribution by the replica method. That operator is constructed of only scalar field. Secondly, we found the sum rule which (Renyi) entanglement entropies of those local operators obey. Those local operators are located separately. Moreover we argue that (Renyi) entanglement entropies of specific operators in conformal field theories are given by (Renyi) entanglement entropies of binomial distribution. These specific operators are constructed of single-species operator. We also argue that general operators obey the sum rule which we mentioned above.

44 pages, 14 figures, v2 references added

References in corpus (10)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Thermodynamical Property of Entanglement Entropy for Excited States
• Entanglement of low-energy excitations in Conformal Field Theory
• Evolution of entanglement after a local quench
• Entanglement Entropy in the O(N) model
• Weak Field Black Hole Formation in Asymptotically AdS Spacetimes
• Universal entanglement entropy in 2D conformal quantum critical points
• Spin-charge separation in two-component Bose-gases
• Measuring Black Hole Formations by Entanglement Entropy via Coarse-Graining
• Dynamics of holographic thermalization

Cited by in corpus (16)

• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• Entanglement negativity after a global quantum quench
• Quantum Entanglement of Localized Excited States at Finite Temperature
• Nonlocal probes of thermalization in holographic quenches with spectral methods
• Rényi entropy of locally excited states with thermal and boundary effect in 2D CFTs
• Left-Right Entanglement Entropy of Boundary States
• Scattering effect on entanglement propagation in RCFTs
• Capacity of Entanglement in Local Operators
• Quantum Entanglement of Locally Excited States in Maxwell Theory
• Entanglement Entropy of Disjoint Regions in Excited States : An Operator Method
• Entanglement Entropy and Mutual Information of Circular Entangling Surfaces in 2 + 1-dimensional Quantum Lifshitz Model
• Subsystem distance after a local operator quench
• Quantum dimensions from local operator excitations in the Ising model
• Non-Gaussianity of Entanglement Entropy and Correlations of Composite Operators
• Subsystem complexity after a local quantum quench
• Entanglement spreading after local and extended excitations in a free-fermion chain