In recent years there has been a growing interest in treating many-body systems as Bell scenarios, where lattice sites play the role of distant parties and only near-neighbor statistics are accessible. We investigate contextuality arising from three Bell scenarios in infinite, translation-invariant 1D models: nearest-neighbor with two dichotomic observables per site; nearest- and next-to-nearest neighbor with two dichotomic observables per site, and nearest-neighbor with three dichotomic observables per site. For the first scenario, we give strong evidence that it cannot exhibit contextuality, not even in non-signaling physical theories beyond quantum mechanics. For the second one, we identify several low-dimensional models that reach the ultimate quantum limits, paving the way for self-testing ground states of quantum many-body systems. For the last scenario, which generalizes the Heisenberg model, we give strong evidence that, in order to exhibit contextuality, the dimension of the local quantum system must be at least 3.

近年来，人们越来越有兴趣将多体系统视为贝尔场景，其中晶格站点扮演远方的角色，只有近邻的统计数据可用。我们在无限的、平移不变的 1D 模型中研究由三个贝尔场景产生的上下文关系：每个站点具有两个二分可观测的最近邻；最近邻和次近邻，每个站点有两个二分可观察对象，最近邻居每个站点有三个二分可观察对象。对于第一种情况，我们给出了强有力的证据表明它不能表现出情境性，即使在量子力学之外的非信号物理理论中也是如此。对于第二个，我们确定了几个达到极限量子极限的低维模型，为量子多体系统的自测基态铺平了道路。