A universal approach to Renyi entropy of multiple disjoint intervals

Abstract

We develop a general theory for computing the Renyi entropy with general multiple disjoint intervals from the swapping operations. Our theory is proposed based on the fact that we have observed the resemblance between the replica trick in quantum field theory and the swapping operation. Consequently, the Renyi entropy can be obtained by evaluating the expectation values of the swapping operator. As an application, we study the Renyi entropy of a one-dimensional transverse-field Ising model for two, three and four disjoint intervals. As the system is at the critical point, our computations of the Renyi entropy are consistent with the analytical results from the conformal field theory. Moreover, our methods can go beyond the critical regime of the Ising model.

References in corpus (17)

• Quantum entanglement
• Entanglement entropy and conformal field theory
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Holographic Entanglement Entropy: An Overview
• On quantum Renyi entropies: a new generalization and some properties
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Entanglement entropy of two disjoint intervals in conformal field theory
• Form factors of branch-point twist fields in quantum integrable models and entanglement entropy
• The Gravity Dual of Renyi Entropy
• Entanglement entropy of two disjoint intervals in conformal field theory II
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Entanglement entropy of two disjoint blocks in XY chains
• Entanglement entropy of two disjoint blocks in critical Ising models
• On Rényi entropies of disjoint intervals in conformal field theory
• Entanglement of two blocks of spins in the critical Ising model
• Charge imbalance resolved Rényi negativity for free compact boson: Two disjoint interval case
• Scaling of finite size effect of $\alpha$-Rényi entropy in disjointed intervals under dilation