Entanglement Negativity for Disjoint Intervals in the Ising and Free Compact Boson Conformal Field Theories

Entanglement negativity is a quantitative measure of entanglement between two parts of a system that is in a mixed state. For conformal field theories (CFTs), entanglement negativity captures fundamental characteristics of the CFT such as the central charge and operator content. In this work, we compute the replicated logarithmic negativity for multiple disjoint intervals for the Ising, free compactified boson, and the free fermion CFTs. In contrast to standard approaches using the correlation function of twist fields, our approach relies on exact computation of the partition function corresponding to theories on higher-genus Riemann surfaces and is more suitable when the number of subsystems is larger than 2. We demonstrate that these partition functions are well behaved under changes in genus through smooth deformations of the intervals. Finally, we compare our results with numerical results obtained using the density matrix renormalization group technique for appropriate lattice regularizations of the CFTs.