Department of Chemistry, Columbia University, New York, New York 10027, USA.
Department of Physics, Columbia University, New York, New York 10027, USA.
Phys Rev Lett. 2015 Mar 13;114(10):100601. doi: 10.1103/PhysRevLett.114.100601. Epub 2015 Mar 11.
We study the infinite temperature dynamics of a prototypical one-dimensional system expected to exhibit many-body localization. Using numerically exact methods, we establish the dynamical phase diagram of this system based on the statistics of its eigenvalues and its dynamical behavior. We show that the nonergodic phase is reentrant as a function of the interaction strength, illustrating that localization can be reinforced by sufficiently strong interactions even at infinite temperature. Surprisingly, within the accessible time range, the ergodic phase shows subdiffusive behavior, suggesting that the diffusion coefficient vanishes throughout much of the phase diagram in the thermodynamic limit. Our findings strongly suggest that Wigner-Dyson statistics of eigenvalue spacings may appear in a class of ergodic but subdiffusive systems.
我们研究了一个典型的一维系统的无限温度动力学，该系统预计会表现出多体局域化现象。我们使用数值精确的方法，根据系统本征值的统计数据及其动力学行为，建立了该系统的动力学相图。我们表明，非遍历相作为相互作用强度的函数是再入的，这表明即使在无限温度下，足够强的相互作用也可以增强局域化。令人惊讶的是，在可访问的时间范围内，遍历相表现出亚扩散行为，这表明在热力学极限下，扩散系数在相图的大部分区域中消失。我们的发现强烈表明，本征值间距的维格纳-狄森统计可能出现在一类遍历但亚扩散的系统中。
