发表机构
Harvard University; University of Chicago（哈佛大学; 芝加哥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
我们提出一种自举框架，通过扩展算子代数以包含无序变量，直接对无序平均可观测量给出严格界限，无需采样，并应用于随机横向场伊辛模型，获得紧致界限并利用自举间隙描绘相图。
AI 中文摘要
我们提出一个自举框架，该框架为具有淬火无序的量子系统的基态可观测量提供严格的双侧界限。关键思想是将算子代数扩展到包含经典无序变量，并通过一组矩来编码无序分布。该方法直接对有限或无限晶格系统以及任意无序分布的无序平均期望值进行界限。与传统方法相比，我们无需对无序实现进行采样，这使我们能够充分利用那些仅平均成立而非对每个无序实现成立的对称性。此外，我们展示了多副本算子可用于访问无序涨落，例如可观测量的方差。我们将该方法应用于具有离散、均匀和高斯无序的一维随机横向场伊辛模型（RTFIM），获得了无序平均基态能量密度和短程自旋-自旋关联函数的紧致界限，以及能量密度无序方差的界限。此外，我们展示了无序平均基态能量密度的上界与下界之差（我们称之为自举间隙）可用于描绘RTFIM的相图。在弱无序下，自举间隙在顺磁和铁磁相内小而平坦，进入格里菲斯区域时增大，并沿临界线达到峰值。
英文摘要
We present a bootstrap framework that yields rigorous two-sided bounds on ground-state observables of quantum systems with quenched disorder. The key idea is to extend the operator algebra to include classical disorder variables and to encode the disorder distribution through a set of moments. The method directly bounds disorder-averaged expectation values for finite or infinite lattice systems and for arbitrary disorder distributions. In contrast to conventional approaches, we do not need to sample disorder realizations, which enables us to make thorough use of symmetries that hold only on average rather than for each disorder realization. Additionally, we show that multi-replica operators can be used to access disorder fluctuations such as the variance of an observable. We apply the method to the one-dimensional random transverse-field Ising model (RTFIM) with discrete, uniform, and Gaussian disorder, obtaining tight bounds on the disorder-averaged ground-state energy density and short-range spin-spin correlators, as well as bounds on the disorder variance of the energy density. Additionally, we show that the difference between the upper and lower bounds on the disorder-averaged ground-state energy density, which we term the bootstrap gap, can be used to map out the phase diagram of the RTFIM. The bootstrap gap is small and flat within the paramagnetic and ferromagnetic phases at weak disorder, grows upon entering the Griffiths regions, and peaks along the critical line.
Comments10 pages, 6 figures
