2021/08/31 by Kévin Hémery, Frank Pollmann, Adam Smith
Mathematics · Physics and Astronomy · #Artificial intelligence #Cluster analysis #Computer science #Eigenvalues and eigenvectors #Graph #Logarithm #Mathematics #Matrix product state #Opinion Dynamics and Social Influence #Pairwise comparison #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Statistical physics #Theoretical computer science #cond-mat.dis-nn #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.105.064202
10 pages, 9 figures
openalex created_date 2021/08/16 · arxiv created 2021/09/15 · openalex publication_date 2022/02/04 · arxiv updated 2022/02/16 · openalex updated_date 2026/08/06
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.