强关联电子系统中的量子蒙特卡洛模拟

Strongly correlated electron system is the main focus of condensed matter physics. It includes vast fields such as unconventional superconductivity, topological state of matter, quantum spin liquid and spin ice, frustrated magnets, heavy fermion metal and superconductor, etc. To study such systems, large-scale quantum Monte Carlo simulations have becoming powerful and indispensable numerical technique to obtain new insights and quantitative understandings, as traditional mean-field-like and perturbation-based analytical approaches cannot tackle such strongly correlated systems in a controlled manner. In this project, we plan to employ large-scale quantum Monte Carlo simulations to study the novel physics in strongly correlated electron systems, including the quantum phase transition and possible spin liquid state in the strongly correlated Dirac fermion systems, new topological invariant that can be used to characterize interacting topological state of matter, static and dynamic properties of quantum phase transitions and in unfrustrated quantum magnetic systems, as well as the emergent quantum spin liquid and spin ice in the frustrated magnetic systems. Based on our numerical results and theoretical development, we hope to further interact and guide experimental development in strongly correlated electron systems.

关于强关联的电子系统的研究是凝聚态物理学研究的主要方向，它的范围涵盖非常规超导体，拓扑绝缘体与超导体，量子自旋液体和自旋冰，阻挫磁体，重电子金属和超导体等等领域。了解这些系统的性质是理论凝聚态物理研究的主要课题，但是由于这些系统往往及其复杂，存在着很多自由度，而且自由度之间具有强关联的相互作用，展现着量子物理学的效应，传统的解析的方法难以提供定量的结果。在这样的情况下，随着计算机性能的突飞猛进，以量子蒙特卡洛为代表的数值方法取而代之地成为了定量研究强关联电子系统的利器。本项目的研究工作是使用大规模量子蒙特卡洛模拟， 通过编写计算机程序，借助超级计算机进行大规模并行计算，从而精确地研究强关联的电子系统中涌现出的各种奇妙的物质形态。重点是强关联的费米子体系中的量子相变和可能存在的量子自旋液体、相互作用下的拓扑物态，和强关联的自旋体系中的量子磁学相变以及阻挫磁体中涌现出的量子自选液体和自旋冰。

在本项目中《强关联电子系统中的量子蒙特卡洛模拟》，我们运用大规模量子蒙特卡洛数值模拟方法，研究了强关联电子系统中的许多困难问题，取得了一些关键数据和重要结果，包括，相互作用驱动拓扑相变、巡游电子量子临界行为、阻挫磁体和量子自旋液体、去禁闭量子临界点的谱学行为等等。同时在计算方法的发展方面，也提出来自学习蒙特卡洛算法，动量空间行列式蒙特卡洛算法等等，推动了量子多体计算领域的进步。

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