Entanglement R\'enyi Negativity across the Finite-Temperature Transition in the O(3) Universality Class

TL;DR

This study uses quantum Monte Carlo simulations to analyze the behavior of Rènyi negativity at the finite-temperature phase transition in the O(3) universality class, revealing that entanglement obeys an area law and its derivatives encode critical scaling.

Contribution

First to investigate Rènyi negativity across a thermal critical point with continuous symmetry, showing entanglement vanishes at criticality while derivatives reflect universal scaling.

Findings

Negativity follows an area law at the critical point.

Temperature derivative of negativity scales with specific heat.

Entanglement is insensitive to thermal criticality, but its derivatives reveal universal behavior.

Abstract

The fate of quantum entanglement at finite-temperature phase transitions remains an open question, particularly for continuous symmetry breaking where zero-temperature Goldstone modes generate long-range correlations. Using large-scale quantum Monte Carlo simulations, we investigate the third R\'enyi negativity across the O(3) transition in the three-dimensional Heisenberg antiferromagnet. The first such study for a thermal critical point with continuous symmetry. We uncover two fundamental results. First, the negativity exhibits a pure area law at the critical point, with the subleading constant term vanishing within statistical uncertainty. This demonstrates that thermal fluctuations completely destroy the long-range entanglement present at zero temperature. The divergent classical correlation length leaves no imprint on quantum entanglement itself. Second, despite this absence of singular behavior in the negativity, its temperature derivative follows the exact scaling of the specific heat, yielding critical exponents -{\alpha}/{\nu}=0.190(1) and 1/{\nu}=1.350(5) in precise agreement with the O(3) universality class. Our work establishes that while quantum entanglement is blind to thermal criticality, its thermodynamic derivatives encode the full universal scaling, revealing an unexpected connection between entanglement and classical phase transitions. Furthermore, this also provides further evidence that R\'enyi negativity can still effectively shield classical correlations in systems with continuous symmetry.