Identifying correlation clusters in many-body localized systems

Hémery, Kévin; Pollmann, Frank; Smith, Adam

Abstract

We introduce techniques for analyzing 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 analyze 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 nonequilibrium dynamics 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.

Citation

Hémery, K., Pollmann, F., & Smith, A. (2022). Identifying correlation clusters in many-body localized systems. Physical Review B, 105(6), Article 064202. https://doi.org/10.1103/physrevb.105.064202

• Journal Article Type: Article
• Acceptance Date: Jan 19, 2022
• Online Publication Date: Feb 4, 2022
• Publication Date: Feb 1, 2022
• Deposit Date: Mar 21, 2022
• Publicly Available Date: Mar 28, 2022
• Journal: Physical Review B
• Print ISSN: 2469-9950
• Electronic ISSN: 2469-9969
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 105
• Issue: 6
• Article Number: 064202
• DOI: https://doi.org/10.1103/physrevb.105.064202
• Public URL: https://nottingham-repository.worktribe.com/output/7611108
• Publisher URL: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.105.064202