Novel approaches to interacting and disordered systems

无序量子系统在现代凝聚态物理的理论发展中继续发挥着关键作用。最初，这是由于安德森在1958年认识到凝聚态物质的量子波动性质可以导致抑制经典预期的电荷传输机制的干涉效应-安德森局域化的诞生。在安德森的论文中，已经讨论了多体效应如何影响这种情况。在过去的十年中，随着计算能力的提高，甚至对于相互作用的系统，也可以构建有意义的大希尔伯特空间，这种无序和多体物理学的相互作用受到了很多关注，但仍然局限于小系统尺寸。真正需要的是一种新的方法来解决基本的薛定谔方程。最近，机器学习和深度学习已经成为使用人工智能策略来预测数值实验结果的数值技术。因此，似乎可以使用DL技术来加速此类稀疏矩阵码，以针对非常大的系统尺寸构建良好近似的本征态。

Disordered quantum systems continue to play a key role in theoretical developments of modern condensed matter physics. Originally, this is due to Anderson's realization in 1958 that the quantum wave nature of condensed matter can lead to interference effects that suppress the classically expected charge transport mechanisms - the birth of Anderson localization. Already in Anderson's paper, it was discussed how the situation might be influenced by many-body effects. In the last decade, following the increase in computational power to allow the construction of meaningfully large Hilbert spaces even for interacting systems, this interplay of disorder and many-body physics has received much attention but remains restricted to small system sizes. What really is needed is a novel approach at solving the underlying Schrödinger equations. Recently, machine learning and deep learning have emerged as numerical techniques that use strategies of artificial intelligence to predict outcomes of numerical experiments. It therefore seems possible to use DL techniques to speed up such sparse matrix codes to construct well-approximated eigenstates for very large system size.