Entanglement negativity in the critical Ising chain

TL;DR

This paper investigates the scaling behavior of entanglement negativity in the critical Ising chain, comparing tensor network calculations with conformal field theory predictions, and analyzing finite size effects for disjoint blocks.

Contribution

It provides a detailed comparison between tensor network results and CFT predictions for entanglement negativity in the critical Ising model, including finite size correction analysis.

Findings

Tensor network calculations agree with CFT for adjacent blocks.

Finite size corrections are necessary for disjoint blocks.

Finite length of blocks affects the entanglement negativity scaling.

Abstract

We study the scaling of the traces of the integer powers of the partially transposed reduced density matrix and of the entanglement negativity for two spin blocks as function of their length and separation in the critical Ising chain. For two adjacent blocks, we show that tensor network calculations agree with universal conformal field theory (CFT) predictions. In the case of two disjoint blocks the CFT predictions are recovered only after taking into account the finite size corrections induced by the finite length of the blocks.