2$-R\'enyi CCNR Negativity of Compact Boson for multiple disjoint intervals

• Main Author: Gaur, Himanshu
• Format: Journal Article
• Language: English
• Published: 12-11-2024
• Subjects: Physics - High Energy Physics - Theory; Physics - Quantum Physics; Physics - Statistical Mechanics
• DOI: 10.48550/arxiv.2411.07698

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.