# Many-body localization transition through pairwise correlations

## TL;DR

This paper studies the many-body localization transition in a disordered Heisenberg spin chain using simple pairwise correlation measures, locating the critical point through finite size scaling and derivatives of correlations.

## Contribution

It introduces a method to identify the MBL transition using only one- and two-point correlation functions without needing multipartite entanglement or large system segments.

## Key findings

- Critical point at h_c/J = 3.8 from global entanglement.
- Two-point correlation derivatives pinpoint transition in h_c/J ∈ [3,4].
- Simple measures effectively detect MBL transition.

## Abstract

We investigate the phenomenon of spatial many-body localization (MBL) through pairwise correlation measures based on one and two-point correlation functions. The system considered is the Heisenberg spin-1/2 chain with exchange interaction $J$ and random onsite disorder of strength $h$. As a representative pairwise correlation measure obtained from one-point functions only, we use global entanglement. Through its finite size scaling analysis, we locate the MBL critical point at $h_{c}/J = 3.8$. As for measures involving two-point functions, we analyze pairwise geometric classical, quantum, and total correlations. Similarly to what happens for continuous quantum phase transitions, it is the derivatives of these two-point correlation measures that identify the MBL critical point, which is found to be in the range $h_{c}/J \in \left[3,4\right]$. Our approach relies on very simple measures that do not require access to multipartite entanglement or large portions of the system.