Charge imbalance resolved R\'enyi negativity for free compact boson: Two disjoint interval case

TL;DR

This paper analyzes the charge imbalance resolution of Rnyi negativity in a 1+1D free compact boson with U(1) symmetry, deriving analytical expressions and validating them numerically against a tight-binding model.

Contribution

It introduces a method to decompose Rnyi negativity into charge sectors for a free compact boson, including analytical derivations and numerical validation.

Findings

Derived multi-charged and charged Rnyi negativity moments.

Obtained charge imbalance resolved Rnyi negativity via Fourier transform.

Validated results with numerical simulations of a tight-binding model.

Abstract

In this paper, we study the symmetry decomposition of R\'enyi negativity into charge imbalance sectors for the 1+1 dimensional free compact boson field with a global U(1) symmetry in the ground state for the case of two disjoint intervals. We obtain multi-charged and charged R\'enyi negativity moments by computing the four-point correlator of flux-generating vertex operators on the Riemann surface. We then obtain charge imbalance resolved R\'enyi negativity by taking the Fourier transform of the charged moments. Finally, we match our results against the tight-binding model as a numerical check.