$2$-Rényi CCNR Negativity of Compact Boson for multiple disjoint intervals

Abstract

We investigate mixed-state bipartite entanglement between multiple disjoint intervals using the computable cross-norm criterion (CCNR). We consider entanglement between a single interval and the union of remaining disjoint intervals, and compute $2$-Rényi CCNR negativity for $2$d massless compact boson. The expression for $2$-Rényi CCNR negativity is given in terms of cross-ratios and Riemann period matrices of Riemann surfaces involved in the calculation. In general, the Riemann surfaces involved in the calculation of $n$-Rényi CCNR negativity do not possess a $Z_n$ symmetry. We also evaluate the Reflected Rényi entropy related to the $2$-Rényi CCNR negativity. This Reflected Rényi entropy is a universal quantity. We extend these calculations to the $2$d massless Dirac fermions as well. Finally, the analytical results are checked against the numerical evaluations in the tight-binding model and are found to be in good agreement.

V2: 30 pages, 11 figures, improved presentation and new references added

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