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Review Article
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Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications
- Zi-Xiang Li1,2, and Hong Yao1,3
- Vol. 10:337-356 (Volume publication date March 2019) https://doi.org/10.1146/annurev-conmatphys-033117-054307
- First published as a Review in Advance on December 19, 2018
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Copyright © 2019 by Annual Reviews. All rights reserved
Abstract
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.
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