Global and short-range entanglement properties in excited, many-body localized spin chains

TL;DR

This paper investigates how short-range and global entanglement measures can serve as indicators of many-body localization in disordered spin chains, demonstrating their effectiveness through numerical analysis of spin-1/2 and spin-1 systems.

Contribution

It extends the use of negativity as an entanglement measure to higher local dimensions and demonstrates its utility in predicting MBL phases in spin-1 systems.

Findings

Negativity behaves similarly to concurrence in MBL detection.

Negativity can be extended to higher local spin systems.

Geometric entanglement acts as a complementary MBL indicator.

Abstract

We explore the use of short-range entanglement measures, such as concurrence and negativity, and global entanglement measures such as geometric entanglement, as indicators of many-body localization (MBL) in the spectra of disordered spin systems. From the perspective of entanglement monogamy, the two types of entanglement behave oppositely in the thermalized and MBL phases. In a recent work, the concurrence of subsystems, a measure of local entanglement, was used in a study of many-body localization in a one-dimensional spin-$1/2$ system (Bera and Lakshminarayan, 2016). We show numerically that the negativity displays notably similar behavior for this system, with the advantage that it can also be extended to systems of higher local dimension. We then demonstrate this extension in practice by using it to predict the existence of an MBL phase in a disordered a spin-1 system. In terms of global entanglement, the geometric entanglement of both spin-$1/2$ and spin-1 systems is also shown to behave as a complementary indicator of the MBL phenomenon.