R\'enyi entropy and negativity for massless Dirac fermions at conformal interfaces and junctions

TL;DR

This paper analyzes the entanglement properties of a (1+1)-dimensional conformal field theory with multiple massless Dirac fermions connected at a junction, deriving universal formulas for entanglement measures and confirming them numerically.

Contribution

It introduces a systematic method to compute Re9nyi entropies and negativity in multi-wire conformal junctions, providing exact universal prefactors.

Findings

Entanglement measures grow logarithmically with system size L.

Universal prefactors depend on junction and bipartition details.

Numerical tests confirm analytical predictions.

Abstract

We investigate the ground state of a (1+1)-dimensional conformal field theory built with $M$ species of massless free Dirac fermions coupled at one boundary point via a conformal junction/interface. Each CFT represents a wire of finite length $L$. We develop a systematic strategy to compute the R\'enyi entropies for a generic bipartition between the wires and the entanglement negativity between two non-complementary sets of wires. Both these entanglement measures turn out to grow logarithmically with $L$ with an exactly calculated universal prefactor depending on the details of the junction and of the bipartition. These analytic predictions are tested numerically for junctions of free Fermi gases, finding perfect agreement.