The intriguing phenomenon of many-body localization (MBL) has attracted significant interest recently, but a complete characterization is still lacking. In this work, we introduce the total correlations, a concept from quantum information theory capturing multi-partite correlations, to the study of this phenomenon. We demonstrate that the total correlations of the diagonal ensemble provides a meaningful diagnostic tool to pin-down, probe, and better understand the MBL transition and ergodicity breaking in quantum systems. In particular, we show that the total correlations has sub-linear dependence on the system size in delocalized, ergodic phases, whereas we find that it scales extensively in the localized phase developing a pronounced peak at the transition. We exemplify the power of our approach by means of an exact diagonalization study of a Heisenberg spin chain in a disordered field.
@article{arxiv.1504.06872,
title = {Total correlations of the diagonal ensemble herald the many-body localization transition},
author = {J. Goold and C. Gogolin and S. R. Clark and J. Eisert and A. Scardicchio and A. Silva},
journal= {arXiv preprint arXiv:1504.06872},
year = {2015}
}