Exact diagonalization at the petaflop scale

精确对角化（艾德）是一种无偏的、通用的方法，用于研究各种量子多体系统，从量子化学和核结构计算到凝聚态物理和超冷原子气体中的相关系统。在该项目的第一个资助期内，在研究单位1807，我们已经成功地开发了一个灵活的消息传递接口（MPI）为基础的量子自旋模型的并行精确对角化代码。我们已经将这个和相关的代码应用于几个当前的问题，在挫折量子磁性和相关的费米子，并开始在2+1时空维度的量子临界点的能量谱的活动。该项目在下一个资助期的目的是进一步发展和应用量子自旋和费米晶格模型的最新艾德框架，第二步也是简单的量子场论。具体来说，我们希望实现谱函数和真实的时间演化功能，以及更大的局部希尔伯特空间，包括费米子。然后，我们将把这个代码应用于各种晶格上的海森堡-基塔耶夫模型的谱函数，并绘制出各种建议的自旋液体波函数与Kagome海森堡反铁磁体和其他假定的量子自旋液体的重叠。此外，我们想追求场论光谱方法和研究费米子晶格模型的Gross-Neveu普适性类，或设计师哈密顿可能显示deconfined量子临界点。作为一个有趣的新的和补充的途径，我们想研究直接哈密顿截断方案的量子场论使用我们的大规模艾德技术。

Exact diagonalization (ED) is an unbiased and versatile method to study a large variety of quantum many-body systems, ranging from quantum chemistry and nuclear structure calculations to correlated systems in condensed matter physics and ultracold atomic gases. In the first funding period of this project within the research unit 1807 we have successfully developed a flexible message-passing interface (MPI) based parallel exact diagonalization code for quantum spin models. We have applied this and related codes to several current problems in frustrated quantum magnetism and correlated fermions, and started an activity on energy spectroscopy of quantum critical points in 2+1 space-time dimensions. The purpose of this project in the next funding period is to further develop and apply a state-of-theart ED framework for quantum spin and fermionic lattice models, and in a second step also for simple quantum field theories. Specifically we want to implement spectral function and real- time evolution functionality, as well as a larger set of local Hilbert spaces, including fermions. We will then apply this code to spectral functions of Heisenberg-Kitaev models on various lattices, and to map out the overlaps of various proposed spin liquid wave functions to the Kagome Heisenberg antiferromagnet and other putative quantum spin liquids. Further we want to pursue the field theory spectroscopy approach and study fermionic lattice models in the Gross-Neveu universality class, or designer Hamiltonians possibly displaying deconfined quantum critical points. As an interesting novel and complementary avenue we want to investigate direct Hamiltonian truncation schemes of quantum field theories using our large-scale ED technology.