Many-body Localization Transition: Schmidt Gap, Entanglement Length & Scaling

Johnnie Gray, S. Bose, A. Bayat
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引用次数: 27

Abstract

Many-body localization has become an important phenomenon for illuminating a potential rift between non-equilibrium quantum systems and statistical mechanics. However, the nature of the transition between ergodic and localized phases in models displaying many-body localization is not yet well understood. Assuming that this is a continuous transition, analytic results show that the length scale should diverge with a critical exponent $\nu \ge 2$ in one dimensional systems. Interestingly, this is in stark contrast with all exact numerical studies which find $\nu \sim 1$. We introduce the Schmidt gap, new in this context, which scales near the transition with a exponent $\nu > 2$ compatible with the analytical bound. We attribute this to an insensitivity to certain finite size fluctuations, which remain significant in other quantities at the sizes accessible to exact numerical methods. Additionally, we find that a physical manifestation of the diverging length scale is apparent in the entanglement length computed using the logarithmic negativity between disjoint blocks.
多体定位跃迁:施密特间隙、纠缠长度和尺度
多体局域化已成为揭示非平衡量子系统与统计力学之间潜在裂缝的重要现象。然而,在显示多体局部化的模型中,遍历阶段和局部阶段之间的过渡的性质尚未得到很好的理解。假设这是一个连续的过渡,分析结果表明,在一维系统中,长度尺度应该以一个临界指数$\nu \ge 2$发散。有趣的是,这与所有精确的数值研究发现$\nu \sim 1$形成鲜明对比。我们引入Schmidt间隙,在这种情况下是新的,它在转换附近缩放,其指数$\nu > 2$与解析界兼容。我们将此归因于对某些有限尺寸波动的不敏感,这些波动在精确数值方法可达到的尺寸下的其他数量中仍然很重要。此外,我们发现在使用不相交块之间的对数负性计算的纠缠长度中,发散长度尺度的物理表现是明显的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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