Exact diagonalization at the petaflop scale

petaflop 规模的精确对角化

• 批准号: 229100890
• 负责人: Professor Dr. Andreas M. Läuchli
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/229100890?language=en
• 关键词: Exact; diagonalization; petaflop; scale

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.

精确对角化（ED）是研究量子多体系统的一种无偏和通用的方法，从量子化学和核结构计算到凝聚态物理和超冷原子气体的相关系统。在该项目的第一个资助期内，在研究单位1807内，我们成功地开发了一个基于量子自旋模型并行精确对角化代码的灵活消息传递接口（MPI）。我们已经将此代码和相关代码应用于当前受挫量子磁性和相关费米子的几个问题，并开始了2+1时空维度量子临界点能谱的研究活动。这个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子晶格模型的最新ED框架，第二步也用于简单的量子场理论。具体来说，我们希望实现谱函数和实时演化功能，以及更大的局部希尔伯特空间集，包括费米子。然后，我们将此代码应用于各种晶格上的海森堡-基塔耶夫模型的谱函数，并绘制出各种提出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部分。进一步，我们想要追求场论光谱方法，研究Gross-Neveu普惠类中的费米子晶格模型，或者可能显示定义量子临界点的设计哈密顿量。作为一种有趣的新颖和互补的途径，我们希望利用我们的大规模ED技术来研究量子场论的直接哈密顿截断方案。