Many-Body Critical Phase: Extended and Nonthermal

The transition between ergodic and many-body localization (MBL) phases lies at the heart of understanding quantum thermalization of many-body systems. Here, we predict a many-body critical (MBC) phase with finite-size scaling analysis in the one-dimensional extended Aubry-Andre-Harper-Hubbard model, which is different from both the ergodic phase and MBL phase, implying that the quantum system hosts three different fundamental phases in the thermodynamic limit. The level statistics in the MBC phase are well characterized by the so-called critical statistics, and the wave functions exhibit deep multifractal behavior only in the critical region. We further study the half-chain entanglement entropy and thermalization properties and show that the former, in the MBC phase, manifest a volume law scaling, while the many-body states violate the eigenstate thermalization hypothesis. The results are confirmed by the state-of-the-art numerical calculations with system size up to L = 22. This work unveils a novel many-body phase which is extended but nonthermal.

Automated summary

This study predicts a novel many-body critical phase in the one-dimensional model, which exhibits distinct characteristics from both the ergodic phase and the many-body localization phase. The level statistics in this new phase follow critical statistics, the wave functions show multifractal behavior, and the entanglement entropy scales with a volume law. These results challenge the eigenstate thermalization hypothesis and provide new insights into the behavior of many-body systems.