Identifying Correlation Clusters in Many-Body Localized Systems

TL;DR

This paper presents a graph-based clustering method to analyze quantum states in many-body localized systems, successfully identifying phase transitions and dynamic signatures with computational efficiency and experimental relevance.

Contribution

It introduces a novel graph-theoretic clustering approach for analyzing correlation structures in MBL systems, validated against theoretical predictions and applicable to large-scale experiments.

Findings

Reproduces MBL transition predictions from renormalization group analysis

Identifies logarithmic entanglement growth in MBL dynamics

Provides computationally efficient tools compatible with experimental data

Abstract

We introduce techniques for analysing the structure of quantum states of many-body localized (MBL) spin chains by identifying correlation clusters from pairwise correlations. These techniques proceed by interpreting pairwise correlations in the state as a weighted graph, which we analyse using an established graph theoretic clustering algorithm. We validate our approach by studying the eigenstates of a disordered XXZ spin chain across the MBL to ergodic transition, as well as the non-equilibrium dyanmics in the MBL phase following a global quantum quench. We successfully reproduce theoretical predictions about the MBL transition obtained from renormalization group schemes. Furthermore, we identify a clear signature of many-body dynamics analogous to the logarithmic growth of entanglement. The techniques that we introduce are computationally inexpensive and in combination with matrix product state methods allow for the study of large scale localized systems. Moreover, the correlation functions we use are directly accessible in a range of experimental settings including cold atoms.