Breakthroughs in two-dimensional van der Waals heterostructures have revealed that twisting creates a moiré pattern that quenches the kinetic energy of electrons, allowing for exotic many-body states. We show that cold atomic, trapped ion, and metamaterial systems can emulate the effects of a twist in many models from one to three dimensions. Further, we demonstrate at larger angles (and argue at smaller angles) that by considering incommensurate effects, the magic-angle effect becomes a single-particle quantum phase transition (including in a model for twisted bilayer graphene in the chiral limit). We call these models “magic-angle semimetals”. Each contains nodes in the band structure and an incommensurate modulation. At magic-angle criticality, we report a nonanalytic density of states, flat bands, multifractal wave functions that Anderson delocalize in momentum space, and an essentially divergent effective interaction scale. As a particular example, we discuss how to observe this effect in an ultracold Fermi gas.

二维范德华异质结构的突破表明，扭曲会形成莫尔条纹，从而淬灭电子的动能，从而产生奇异的多体态。我们表明，冷原子，捕获离子和超材料系统可以在许多模型中从一维到三维模拟扭曲的影响。此外，我们在更大的角度（并以较小的角度争论）证明了通过考虑不相称的效应，魔角效应变成了单粒子量子相变（包括在手性极限中的扭曲双层石墨烯模型中）。我们称这些模型为“魔角半金属”。每个节点都包含频带结构中的节点和不相称的调制。在魔角临界状态下，我们报告了状态，平坦带，安德森在动量空间中离域的多重分形波函数，以及基本不同的有效相互作用尺度。作为一个特定的例子，我们讨论如何在超冷费米气体中观察这种效应。