Wang Yucheng, Cheng Chen, Liu Xiong-Jun, Yu Dapeng
Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China.
International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China.
Phys Rev Lett. 2021 Feb 26;126(8):080602. doi: 10.1103/PhysRevLett.126.080602.
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-André-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.
遍历相和多体局域化（MBL）相之间的转变是理解多体系统量子热化的核心所在。在此，我们通过对一维扩展奥布里 - 安德烈 - 哈珀 - 哈伯德模型进行有限尺寸标度分析，预测了一个多体临界（MBC）相，它既不同于遍历相也不同于MBL相，这意味着在热力学极限下量子系统存在三种不同的基本相。MBC相中的能级统计由所谓的临界统计很好地刻画，并且波函数仅在临界区域表现出深度多重分形行为。我们进一步研究了半链纠缠熵和热化性质，结果表明，在MBC相中，前者呈现体积律标度，而多体态违反了本征态热化假设。高达L = 22的系统规模的最新数值计算证实了这些结果。这项工作揭示了一种新型的扩展但非热的多体相。
