标题： $2$-Rényi CCNR 负性量：多段不连通区间紧致玻色子的 显示英文标题

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

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 $2$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. 显示英文摘要

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 $2$-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.