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Fermions are basic building blocks in the standard model. Interactions among these elementary particles determine how they assemble and consequently form various states of matter in our nature. Simulating fermionic degrees of freedom is also a central problem in condensed matter physics and quantum chemistry, which is crucial to understanding high-temperature superconductivity, quantum magnetism and molecular structure and functionality. However, simulating interacting fermions by classical computing generically face the minus sign problem, encountering the exponential computation complexity. Ultracold atoms provide an ideal experimental platform for quantum simulation of interacting fermions. This highly-controllable system enables the realizing of nontrivial fermionic models, by which the physical properties of the models can be obtained by measurements in experiment. This deepens our understanding of related physical mechanisms and helps determine the key parameters. In recent years, there have been versatile experimental studies on quantum ground state physics, finite temperature thermal equilibrium, and quantum many-body dynamics, in fermionic quantum simulation systems. Quantum simulation offers an access to the physical problems that are intractable on the classical computer, including studying macroscopic quantum phenomena and microscopic physical mechanisms, which demonstrates the quantum advantages of controllable quantum systems. This paper briefly introduces the model of interacting fermions describing the quantum states of matter in such a system. Then we discuss various states of matter, which can arise in interacting fermionic quantum systems, including Cooper pair superfluids and density-wave orders. These exotic quantum states play important roles in describing high-temperature superconductivity and quantum magnetism, but their simulations on the classical computers have exponentially computational cost. Related researches on quantum simulation of interacting fermions in determining the phase diagrams and equation of states reflect the quantum advantage of such systems.
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Keywords:
- quantum simulation /
- interacting fermions /
- cold atoms /
- optical lattice
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[1] Giorgini S, Pitaevskii L P, Stringari S 2008 Rev. Mod. Phys. 80 1215
Google Scholar
[2] McArdle S, Endo S, Aspuru-Guzik A, Benjamin S C, Yuan X 2020 Rev. Mod. Phys. 92 015003
Google Scholar
[3] Boll M, Hilker T A, Salomon G, Omran A, Nespolo J, Pollet L, Bloch I, Gross C 2016 Science 353 1257
Google Scholar
[4] Mazurenko A, Chiu C S, Ji G, Parsons M F, Kanasz-Nagy M, Schmidt R, Grusdt F, Demler E, Greif D, Greiner M 2017 Nature 545 462
Google Scholar
[5] Mitra D, Brown P T, Guardado-Sanchez E, Kondov S S, Devakul T, Huse D A, Schauß P, Bakr W S 2018 Nat. Phys. 14 173
Google Scholar
[6] Brown P T, Mitra D, Guardado-Sanchez E, Nourafkan R, Reymbaut A, Hébert C D, Bergeron S, Tremblay A M S, Kokalj J, Huse D A, Schauß P, Bakr W S 2019 Science 363 379
Google Scholar
[7] Schreiber M, Hodgman S S, Bordia P, Lüschen H P, Fischer M H, Vosk R, Altman E, Schneider U, Bloch I 2015 Science 349 842
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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[23] Liu X P, Yao X C, Deng Y J, Wang X Q, Wang Y X, Huang C J, Li X P, Chen Y A, Pan J W 2021 Phys. Rev. Lett. 126 185302
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[30] Daley A J, Bloch I, Kokail C, Flannigan S, Pearson N, Troyer M, Zoller P 2022 Nature 607 667
Google Scholar
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