Charged R\'enyi negativity of massless free bosons

TL;DR

This paper derives an exact scaling function for charged moments of the reduced density matrix in a 1+1D free boson CFT, enabling symmetry decomposition of entanglement measures, validated by numerical tests.

Contribution

It provides the first exact analytical expression for charged Rénnyi negativity in a free boson CFT, linking conformal field theory with entanglement symmetry analysis.

Findings

Exact scaling function for four-point fluxed twist field correlator

Analytic formulas for charged moments of partial transpose

Perfect agreement with numerical harmonic chain results

Abstract

In this paper, we consider the computation of charged moments of the reduced density matrix of two disjoint intervals in the $1+1$ dimensional free compactified boson conformal field theory (CFT) by studying the four-point function of the fluxed twist fields. We obtained the exact scaling function of this four-point function and discussed its decompactification limit. This scaling function was used to obtain the charged moments of the partial transpose which we refer as charged R\'enyi negativity. These charged moments and the charged moments of the partial transpose are essential for the problem of symmetry decomposition of the corresponding entanglement measures. We test our analytic formula against exact numerical computation in the complex harmonic chain, finding perfect agreements.