发表机构
Universiteit Leiden; The Hebrew University of Jerusalem; Ulm University（莱顿大学; 耶路撒冷希伯来大学; 乌尔姆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出基于半定规划层级的框架，为格点规范理论基态能量提供严格下界并推广至威尔逊环等可观测量，在(1+1)维和(2+1)维模型中验证，获得高精度认证区间。
AI 中文摘要
规范理论描述了粒子物理标准模型中的基本相互作用，并构建了凝聚态物理中的有效理论。这些理论以难以模拟而著称，通常被正则化为格点规范理论，可通过蒙特卡洛算法或变分方法进行高精度评估。然而，由于符号问题，蒙特卡洛算法并非在所有情况下都适用；而变分方法，无论是量子的还是经典的，只能给出基态能量的上界。其精度关键取决于所选择的试探波函数。在此，我们提出一个基于半定规划层级结构的框架，以产生越来越好的基态能量下界，并将这些界推广到扩展可观测量，如威尔逊环和介子弦。我们通过将算法应用于具有动态费米子物质的(1+1)维$\mathbb{Z}_2$理论及其(2+1)维纯规范版本，展示了数值能力。在两种情况下，我们都获得了基态能量的认证区间。对于具有129个格点的一维系统，认证区间的相对展宽为$0.04\\%$。对于具有97个格点（对应$7 \times 8$晶格）的二维系统，相对展宽为$2.08\\%$。除了能量估计之外，所提出的方法还为短程和长程可观测量提供了严格的界，例如跨越多个方格（plaquette）的威尔逊环以及介子弦的幅度。该方法既可用作多体物理的计算显微镜，也可用于认证量子模拟器的结果。
英文摘要
Gauge theories describe fundamental interactions in the standard model of particle physics and build effective theories in condensed matter physics. Being notoriously hard to simulate, these theories are commonly regularized as lattice gauge theories which can be evaluated with high precision through Monte Carlo algorithms or variational methods. However, Monte Carlo algorithms are not applicable in all regimes due to the sign problem; while variational methods, quantum and classical alike, only give upper-bounds on the ground-state energy. Their precision crucially depends on the chosen ansatz. Here, we present a framework based on a hierarchy of semidefinite programs to yield increasingly good lower-bounds on the ground-state energy and propagate these bounds to extended observables like Wilson loops and mesonic strings. We demonstrate the numerical capabilities by applying the algorithm to a (1+1)-dimensional $\mathbb{Z}_2$ theory with dynamic fermionic matter and its pure-gauge version in (2+1)-dimensions. In both cases, we obtain certified intervals for the ground-state energy. For a one-dimensional system with 129 sites, the certified interval has a relative spread of $0.04\%$. For a two-dimensional system with 97 sites (corresponding to a $7 \times 8$ lattice), the relative spread is $2.08\%$. Beyond energy estimates, the proposed method provides rigorous bounds on both short- and long-range observables such as Wilson loops over multiple plaquettes and the magnitude of the mesonic string. The method can be both used as a computational microscope into many-body physics and a way to certify results of quantum simulators.
Comments14 pages, 10 figures
