Many-body critical phase: extended and nonthermal

TL;DR

This paper predicts a novel many-body critical phase in a one-dimensional model, characterized by multifractal wave functions, volume-law entanglement entropy, and non-thermalizing behavior, distinct from ergodic and localized phases.

Contribution

It introduces and characterizes a new many-body phase that is extended yet non-ergodic, expanding understanding of quantum phase diversity.

Findings

Level statistics follow critical statistics.

Wave functions exhibit multifractality.

Entanglement entropy scales with volume but violates thermalization.

Abstract

The transition between ergodic phase and many-body localization (MBL) phase lies at the heart in understanding quantum thermalization of many-body systems. Here we predict a many-body critical phase in the one-dimensional extended Aubry-Andr\'{e}-Harper-Hubbard model, which is different from both the ergodic phase and MBL phase, implying that the quantum system hosts three different fundamental phases. It is shown that the level statistics in the many-body critical phase are well characterized by the so-called critical statistics, and the wave functions in this phase generally exhibit a multifractal behavior. We further study the half-chain entanglement entropy (EE) and thermalization properties by exact diagonalization, which show that the EE in this critical phase manifest a volume law EE scaling while the many-body states violate the eigenstate thermalization hypothesis. This work unveils a novel many-body phase which is extended but non-ergodic.