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首页> 外文期刊>Physical Review X >Non-Abelian Symmetries and Disorder: A Broad Nonergodic Regime and Anomalous Thermalization
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Non-Abelian Symmetries and Disorder: A Broad Nonergodic Regime and Anomalous Thermalization

机译：非雅芳对称和紊乱：宽阔的非亲子政权和异常的热化

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Previous studies reveal a crucial effect of symmetries on the properties of a single particle moving in a disorder potential. More recently, a phenomenon of many-body localization (MBL) has been attracting much theoretical and experimental interest. MBL systems are characterized by the emergence of quasilocal integrals of motion and by the area-law entanglement entropy scaling of its eigenstates. In this paper, we investigate the effect of a non-Abelian S U ( 2 ) symmetry on the dynamical properties of a disordered Heisenberg chain. While S U ( 2 ) symmetry is inconsistent with conventional MBL, a new nonergodic regime is possible. In this regime, the eigenstates exhibit faster than area-law, but still strongly subthermal, scaling of the entanglement entropy. Using extensive exact diagonalization simulations, we establish that this nonergodic regime is indeed realized in the strongly disordered Heisenberg chains. We use the real-space renormalization group (RSRG) to construct approximate excited eigenstates by tree tensor networks and demonstrate the accuracy of this procedure for systems of sizes up to L = 26 . As the effective disorder strength is decreased, a crossover to the thermalizing phase occurs. To establish the ultimate fate of the nonergodic regime in the thermodynamic limit, we develop a novel approach for describing many-body processes that are usually neglected by the RSRG. This approach is capable of describing 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. Crucially, the probability of finding resonances grows with the system’s size. Even at strong disorder, we can identify a large length scale beyond which resonances proliferate. Presumably, this proliferation would eventually drive the system to a thermalizing phase. However, the extremely long thermalization timescales indicate that a broad nonergodic regime will be observable experimentally. Our study demonstrates that, similar to the case of single-particle localization, 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, well beyond sizes accessible in previous studies.
机译：以前的研究揭示了对称对单颗粒在疾病潜力中移动的性质的关键影响。最近，许多身体定位（MBL）的现象一直吸引了大量的理论和实验兴趣。 MBL Systems的特征在于出现运动的Quasilocal积分以及其特征的区域法纠缠熵缩放。在本文中，我们研究了非阿比越S U（2）对称对紊乱Heisenberg链的动态性质的影响。虽然S U（2）对称性与常规MBL不一致，但是可以进行新的非合理性制度。在这个制度中，特征符表现出比区域法更快，但仍然强烈地分解出纠缠熵。使用广泛的精确对角模拟，我们确立了这种不经紊乱的Heisenberg链中的不良状态。我们使用真实空间重新成型组（RSRG）通过树张量网络构建近似激发的特征符，并展示该过程的尺寸最多尺寸的方法的准确性。随着有效的紊乱强度降低，发生与热化相的交叉发生。为了在热力学限制中建立非精体制度的最终命运，我们开发了一种新的方法，用于描述通常被RSRG忽视的许多身体过程。这种方法能够描述大小L≈2000的系统。我们的特征在于由于这些过程而产生的共振，发现它们涉及在系统尺寸增加时涉及不断增长的旋转。至关重要的是，找到共振的概率随系统的尺寸而生长。即使在强烈的疾病中，我们也可以识别超出其共振增殖的大长度。据推测，这种增殖最终将系统驱动到热化阶段。然而，极长的热化时间尺寸表明，广泛的非精通制度将是实验可观察的。我们的研究表明，类似于单粒子定位的情况，对称控制无序，许多机身系统的动态性质。此处介绍的方法提供了一种多功能的工具，用于描述广泛的无序的许多身体系统，远远超出以前研究的尺寸。

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