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

• URL: http://arxiv.org/abs/2411.07698v1
• Date: Tue, 12 Nov 2024 10:24:50 GMT
• Title: $2$-Rényi CCNR Negativity of Compact Boson for multiple disjoint intervals
• Authors: Himanshu Gaur,
• Abstract summary: We consider entanglement between a single interval and the union of remaining disjoint intervals. We compute $2$-R'enyi CCNR negativity for $2$d massless compact boson.
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• 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 $2$-R\'enyi CCNR negativity for $2$d massless compact boson. The expression for $2$-R\'enyi 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 $n$-R\'enyi CCNR negativity do not possess a $Z_n$ symmetry. We also evaluate the Reflected R\'enyi entropy related to the $2$-R\'enyi CCNR negativity. This Reflected R\'enyi 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.

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