Replicated Entanglement Negativity for Disjoint Intervals in the Ising and Free Compact Boson Conformal Field Theories

Abstract

We calculate the $N$ interval replicated negativity for the Ising and free compact boson conformal field theory using correlation functions of branch point twist fields. For some subset $P\subset N$, this is a calculation of $\mathrm{Tr}({\rho }_{\mathrm{A}}^{{\mathrm{T}}_{\mathrm{P}}}{)}^{\mathrm{n}}$ where $n$ is the replica index. This can be reformulated as a calculation of partition functions over superelliptic Riemann surfaces, and for the models in question, this partition function can be expressed in terms of the period matrix of this surface. We detail how to construct the period matrices for these surfaces, giving an analytic expression for $\mathrm{Tr}({\rho }_{\mathrm{A}}^{{\mathrm{T}}_{\mathrm{P}}}{)}^{\mathrm{n}}$. The results are expressed such that when $P=\varnothing$, which corresponds to calculating the Rényi entropy, the formulas aligns with known results for the $N$ interval Rényi entropy.

24 pages, 10 figures. Fixed some figures and formatting

References in corpus (8)

• Entanglement negativity in quantum field theory
• 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 through conformal interfaces
• Entanglement entropy and negativity of disjoint intervals in CFT: Some numerical extrapolations
• The quantum sine-Gordon model with quantum circuits
• Entanglement entropy in the Ising model with topological defects
• Entanglement of two disjoint intervals in conformal field theory and the 2D Coulomb gas on a lattice

Cited by in corpus (3)

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