Study of many-body localization at ground state and finite temperatures with complex polarization

Many-body localization (MBL) occurs when disorder takes precedence over electron-electron interactions in a lattice. This phenomenon has been extensively studied due to its potential to preserve quantum coherence against thermalization. However, the conventional method for characterizing MBL using the eigenenergy spectrum distribution can be costly. In this presentation, we propose a formula for using complex polarization to detect and characterize MBL in both ground and finite-temperature states. We demonstrate that, even though the complex polarization operator is fundamentally an N-body operator, it can be computed efficiently using Slater determinants. Our findings are showcased using both the disordered spineless model and the disordered Hubbard model. Additionally, we reveal that the MBL transition is associated with transitions in magnetization and metal-insulator behavior.