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<p>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 a 2d 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 <i>n</i>-Rényi CCNR negativity do not possess a <i>Z</i><sub><i>n</i></sub> 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 2d 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.</p>

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2-Rényi CCNR negativity of compact boson for multiple disjoint intervals

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  • 发表日期：

    2025年8月20日

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  • Himanshu Gaur

摘要

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 a 2d 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 Zn 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 2d 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.