多体局部化转换中临界点的特征

'Angel L. Corps, R. Molina, A. Relaño
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引用次数: 10

摘要

经历多体局域化跃迁的无序相互作用自旋链具有两种极限行为,即动力学是混沌的和可积的。然而,它们之间的过渡区域还没有被完全理解。我们在这里提出一个签名,明确地识别一个临界点的可能有限大小的前体,并区分两个不同的过渡阶段。在范式无序的$J_1$-$J_2$模型中,全一维动量分布的对角线涨落相对于其微规范平均值的峰度过剩在这个奇点处是最大的。该最大值的特定值和达到该最大值时的无序强度都随着系统规模的增加而增加,这与典型的有限规模标度所期望的一致。我们完整地描述了模型的短期和长期谱统计量,并发现它们的行为与对角起伏的性质完全相关。对于较低的无序值,我们发现一个混沌区域,在该区域中,索利斯能量一直减小到过渡点,在过渡点处它与海森堡能量相等。对于较大的无序值,谱统计量可以很好地用广义半泊松模型描述,最终导致可积泊松行为。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Signatures of a critical point in the many-body localization transition
Disordered interacting spin chains that undergo a many-body localization transition are characterized by two limiting behaviors where the dynamics are chaotic and integrable. However, the transition region between them is not fully understood yet. We propose here a signature that unambiguously identifies a possible finite-size precursor of a critical point, and distinguishes between two different stages of the transition. The kurtosis excess of the diagonal fluctuations of the full one-dimensional momentum distribution from its microcanonical average is maximum at this singular point in the paradigmatic disordered $J_1$-$J_2$ model. Both the particular value of this maximum and the disorder strength at which it is reached increase with the system size, as expected for a typical finite-size scaling. We completely characterize the short and long-range spectral statistics of the model and find that their behavior perfectly correlates with the properties of the diagonal fluctuations. For lower values of the disorder, we find a chaotic region in which the Thouless energy diminishes up to the transition point, at which it becomes equal to the Heisenberg energy. For larger values of disorder, spectral statistics are very well described by a generalized semi-Poissonian model, eventually leading to the integrable Poissonian behavior.
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