标题： 自洽张量网络方法研究十亿站点以上的关联超莫尔物质 显示英文标题

标题： Self-consistent tensor network method for correlated super-moiré matter beyond one billion sites

摘要： 莫尔超莫尔材料为设计奇异的关联量子物质提供了卓越的平台。 由于需要巨大的计算资源，用实空间建模莫尔系统所需的大量位点仍然是一个巨大的挑战。 超莫尔材料将这一需求推向了极限，其中需要考虑数百万甚至数十亿个位点，这远远超出了传统方法对相互作用系统的处理能力。 在这里，我们建立了一种方法，允许解决达到十亿个位点的系统的关联状态，该方法利用了实空间哈密顿量的张量网络表示和自洽的实空间平均场方程。 我们的方法结合了张量网络核多项式方法与量子张量交叉插值算法，使我们能够求解指数级大小的模型，包括那些单粒子哈密顿量太大而无法显式存储的模型。 我们通过具有空间调制跳跃、多体相互作用和畴壁的超莫尔系统展示了我们的方法，表明它可以访问自洽的对称破缺态和达到十亿个位点的实空间模型的谱函数。 我们的方法提供了解决极其大型相互作用问题的策略，为计算关联超莫尔量子物质提供了一个广泛适用的策略。 显示英文摘要

摘要： Moir\'e and super-moir\'e materials provide exceptional platforms to engineer exotic correlated quantum matter. The vast number of sites required to model moir\'e systems in real space remains a formidable challenge due to the immense computational resources required. Super-moir\'e materials push this requirement to the limit, where millions or even billions of sites need to be considered, a requirement beyond the capabilities of conventional methods for interacting systems. Here, we establish a methodology that allows solving correlated states in systems reaching a billion sites, that exploits tensor-network representations of real-space Hamiltonians and self-consistent real-space mean-field equations. Our method combines a tensor-network kernel polynomial method with quantics tensor cross interpolation algorithm, enabling us to solve exponentially large models, including those whose single particle Hamiltonian is too large to be stored explicitly. We demonstrate our methodology with super-moir\'e systems featuring spatially modulated hoppings, many-body interactions and domain walls, showing that it allows access to self-consistent symmetry broken states and spectral functions of real-space models reaching a billion sites. Our methodology provides a strategy to solve exceptionally large interacting problems, providing a widely applicable strategy to compute correlated super-moir\'e quantum matter.