Nonzero temperature Entanglement Negativity of quantum spin models: Area law, Linked Cluster Expansions and Sudden Death

TL;DR

This paper demonstrates that quantum spin models exhibit an area law for entanglement negativity at all nonzero temperatures, introduces linked cluster expansions for its calculation, and reveals a sudden death phenomenon at finite temperatures.

Contribution

It develops numerical linked cluster expansions for entanglement negativity, providing a new method to analyze quantum spin models at finite temperatures and uncovering the sudden death phenomenon.

Findings

Entanglement negativity obeys an area law at all nonzero temperatures.

Linked cluster expansions agree well with exact diagonalization results.

Negativity exhibits a sudden onset or death at a finite temperature.

Abstract

We show that the bipartite logarithmic entanglement negativity (EN) of quantum spin models obeys an area law at all nonzero temperatures. We develop numerical linked cluster (NLC) expansions for the `area-law' logarithmic entanglement negativity as a function of temperature and other parameters. For one-dimensional models the results of NLC are compared with exact diagonalization on finite systems and are found to agree very well. The NLC results are also obtained for two dimensional XXZ and transverse-field Ising models. In all cases, we find a sudden onset (or sudden death) of negativity at a finite temperature above which the negativity is zero. We use perturbation theory to develop a physical picture for this sudden onset (or sudden death). The onset of EN or its magnitude are insensitive to classical finite-temperature phase transitions, supporting the argument for absence of any role of quantum mechanics at such transitions. On approach to a quantum critical point at $T=0$, negativity shows critical scaling in size and temperature.