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Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications
Annual Review of Condensed Matter Physics ( IF 14.3 ) Pub Date : 2019-03-11 00:00:00 , DOI: 10.1146/annurev-conmatphys-033117-054307
Zi-Xiang Li 1, 2 , Hong Yao 1, 3
Affiliation  

Reliable simulations of correlated quantum systems, including high-temperature superconductors and frustrated magnets, are increasingly desired nowadays to further our understanding of essential features in such systems. Quantum Monte Carlo (QMC) is a unique numerically exact and intrinsically unbiased method to simulate interacting quantum many-body systems. More importantly, when QMC simulations are free from the notorious fermion sign problem, they can reliably simulate interacting quantum models with large system size and low temperature to reveal low-energy physics such as spontaneously broken symmetries and universal quantum critical behaviors. Here, we concisely review recent progress made in developing new sign-problem-free QMC algorithms, including those employing Majorana representation and those utilizing hot-spot physics. We also discuss applications of these novel sign-problem-free QMC algorithms in simulations of various interesting quantum many-body models. Finally, we discuss possible future directions of designing sign-problem-free QMC methods.

中文翻译:


无符号问题的铁离子量子蒙特卡罗:发展与应用

如今,越来越需要对包括高温超导体和受阻磁体在内的相关量子系统进行可靠的仿真,以进一步了解此类系统的基本特征。量子蒙特卡洛(QMC)是一种独特的数值精确且本质上无偏的方法,用于模拟相互作用的量子多体系统。更重要的是,当QMC模拟没有臭名昭著的费米子符号问题时,它们可以可靠地模拟具有大系统尺寸和低温的相互作用的量子模型,以揭示低能物理特性,例如自发破坏的对称性和普遍的量子临界行为。在这里,我们简要地回顾了开发无符号问题的新QMC算法方面的最新进展,包括采用Majorana表示的算法和利用热点物理学的算法。我们还将讨论这些新颖的无符号问题QMC算法在各种有趣的量子多体模型仿真中的应用。最后,我们讨论了设计无符号问题的QMC方法的未来可能方向。

更新日期:2019-03-11
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