Entanglement Renyi negativity across a finite temperature transition: a Monte Carlo study

TL;DR

This study uses quantum Monte Carlo simulations to analyze the behavior of the third Renyi negativity, a measure of mixed-state entanglement, across a finite temperature phase transition in the 2D transverse field Ising model, revealing that entanglement remains short-ranged at criticality.

Contribution

It demonstrates that the area-law coefficient of the Renyi negativity is singular at the transition, while the subleading constant remains zero, indicating short-range entanglement at the critical point.

Findings

Area-law coefficient of Renyi negativity is singular at transition.

Subleading constant of Renyi negativity is zero within error.

Entanglement remains short-ranged at criticality.

Abstract

Quantum entanglement is fragile to thermal fluctuations, which raises the question whether finite temperature phase transitions support long-range entanglement similar to their zero temperature counterparts. Here we use quantum Monte Carlo simulations to study the third Renyi negativity, a generalization of entanglement negativity, as a proxy of mixed-state entanglement in the 2D transverse field Ising model across its finite temperature phase transition. We find that the area-law coefficient of the Renyi negativity is singular across the transition, while its subleading constant is zero within the statistical error. This indicates that the entanglement is short-ranged at the critical point despite a divergent correlation length. Renyi negativity in several exactly solvable models also shows qualitative similarities to that in the 2D transverse field Ising model.