Finite temperature entanglement negativity in conformal field theory

TL;DR

This paper derives the correct universal scaling form for finite temperature entanglement negativity in conformal field theories, correcting previous methods and validating results with numerical simulations.

Contribution

It introduces a novel four-point function approach to accurately compute finite temperature negativity in conformal systems, accounting for the full operator content.

Findings

Universal scaling form depends on the full operator content.

Corrected approach yields results consistent with numerical simulations.

Low and high temperature expansions obtained via operator product expansion.

Abstract

We consider the logarithmic negativity of a finite interval embedded in an infinite one dimensional system at finite temperature. We focus on conformal invariant systems and we show that the naive approach based on the calculation of a two-point function of twist fields in a cylindrical geometry yields a wrong result. The correct result is obtained through a four-point function of twist fields in which two auxiliary fields are inserted far away from the interval, and they are sent to infinity only after having taken the replica limit. In this way, we find a universal scaling form for the finite temperature negativity which depends on the full operator content of the theory and not only on the central charge. In the limit of low and high temperatures, the expansion of this universal form can be obtained by means of the operator product expansion. We check our results against exact numerical computations for the critical harmonic chain.