Entanglement negativity for a free scalar chiral current

TL;DR

This paper derives analytic formulas for entanglement negativity in a free scalar chiral current model, revealing topological contributions and decay behavior, and confirms results with numerical lattice simulations.

Contribution

It provides the first analytic expressions for the moments of the partial transpose and the logarithmic negativity in this model, highlighting symmetry effects on entanglement.

Findings

Analytic formulas for negativity and moments derived.

Topological contributions identified in the small separation limit.

Exponential decay of negativity at large separation confirmed.

Abstract

We study the entanglement negativity for the free, scalar chiral current in two spacetime dimensions, which is a simple model violating the Haag duality in regions with nontrivial topology. For the ground state of the system, both on the line and on the circle, we consider the setups given by two intervals, either adjacent or disjoint. We find analytic expressions for the moments of the partial transpose of the reduced density matrix and the logarithmic negativity. In the limit of small separation distance, this expression yields the same subleading topological contribution occurring in the mutual information. In the limit of large separation distance between the two intervals, the exponential decay of the logarithmic negativity is obtained from its analytic expression. The analytic formulas are checked against exact numerical results from a bosonic lattice model, finding a perfect agreement. We observe that, since the chiral current generates the neutral subalgebra of the full chiral Dirac fermion theory, this analysis highlights how symmetries produce nontrivial features in the entanglement structure that are analogue to those ones already observed in the mutual information for regions with nontrivial topology.