Symmetries play a central role in single-particle localization. Recent research focused on many-body localized (MBL) systems, characterized by new kind of integrability, and by the area-law entanglement of eigenstates. We investigate the effect of a non-Abelian $SU(2)$ symmetry on the dynamical properties of a disordered Heisenberg chain. While $SU(2)$ symmetry is inconsistent with the conventional MBL, a new non-ergodic regime is possible. In this regime, the eigenstates exhibit faster than area-law, but still a strongly sub-thermal scaling of entanglement entropy. Using exact diagonalization, we establish that this non-ergodic regime is indeed realized in the strongly disordered Heisenberg chains. We use real-space renormalization group (RSRG) to construct approximate excited eigenstates, and show their accuracy for systems of size up to $L=26$. As disorder strength is decreased, a crossover to the thermalizing phase occurs. To establish the ultimate fate of the non-ergodic regime in the thermodynamic limit, we develop a novel approach for describing many-body processes that are usually neglected by RSRG, accessing systems of size $L>2000$. We characterize the resonances that arise due to such processes, finding that they involve an ever growing number of spins as the system size is increased. The probability of finding resonances grows with the system size. Even at strong disorder, we can identify a large lengthscale beyond which resonances proliferate. Presumably, this eventually would drive the system to a thermalizing phase. However, the extremely long thermalization time scales indicate that a broad non-ergodic regime will be observable experimentally. Our study demonstrates that symmetries control dynamical properties of disordered, many-body systems. The approach introduced here provides a versatile tool for describing a broad range of disordered many-body systems.
Ergodicity breaking in matrix-product-state effective Hamiltonians
School of Physics and Astronomy, University of Leeds（利兹大学物理与天文学院）；University of Nottingham（诺丁汉大学）；Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham（诺丁汉大学量子非平衡系统数学与理论物理中心）
Thermalization Breakdown and Conductivity Improvement within the Interacting Dynamic Disorder Model
基于Kubo公式框架，发展了最小纠缠典型热态算法，研究了一维无自旋费米子模型中电流-电流关联函数的温度和时间依赖性，同时考虑了电子-电子（e-e）格点间相互作用和经典声子引起的动力学无序.在没有e-e相互作用的情况下，数值结果表明，随时间变化的相关性呈指数衰减，可以与解析推导的结果，即广义Langevin方程的结果进行精确的比较。更重要的是，当存在足够强的电子-电子相互作用时，我们发现在小的动力学无序区存在长时间的关联，这表明热弛豫的破坏，这是一个典型的多体效应。在此基础上，我们表明，这可能是适用于理解的金属类电荷传输和电导率的异常改善相对于在K $_3$ C $_{60}$，有机超导材料的再掺杂实验。
