Topological order and fractionalized excitations in quantum many-body systems

Gu Zhao-Long; Li Jian-Xin

doi:10.7498/aps.73.20240222

Abstract

The Landau Fermi liquid theory and the Ginzburg-Landau phase transition theory stand as two pivotal cornerstones in traditional condensed matter physics, achieving significant success in addressing crucial physical phenomena such as BCS superconductors and liquid helium superfluids. However, marked by the discoveries of the quantum Hall effect and high-temperature superconductivity in the 1980s, it gradually became evident that for a broad class of novel quantum states, such as fractional quantum Hall states and quantum spin liquids, their properties transcend the Landau Fermi liquid theory and Ginzburg-Landau phase transition theory. Topological order and its related concepts of long-range many-body quantum entanglement and fractionalized excitation have become the key concepts to understand these exotic quantum states. Designing and identifying topologically ordered states of matter in quantum materials and quantum simulation systems, and probing and manipulating their fractionalized excitations, are important research directions in modern condensed matter physics. In recent years, great progress has been made in the quantum simulation and manipulation of topological order on highly controllable quantum simulation platforms, such as Rydberg atomic systems, superconducting quantum processors, and two-dimensional moiré superlattices. This article provides a brief overview of recent research advances and challenges in the study of topological order in traditional condensed matter systems and quantum simulation experimental platforms. It also provides prospects for the future developments of this field.

Keywords:

topological order /
long-range many-body quantum entanglement /
fractionalized excitations

Authors and contacts

Gu Zhao-Long¹,
Li Jian-Xin^1,2

1.
National Laboratory of Solid State Microstructures, Department of Physics, Nanjing University, Nanjing 210093, China
2.
Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

Corresponding author: Li Jian-Xin, jxli@nju.edu.cn

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References

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[24]	Cao Y, Fatemi V, Demir A, Fang S, Tomarken S L, Luo J Y, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E, Ashoori R C, Jarillo-Herrero P 2018 Nature 556 80 Google Scholar
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[26]	Neupert T, Santos L, Chamon C, Mudry C 2011 Phys. Rev. Lett. 106 236804 Google Scholar
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Cited By

[1]	Anderson P W 1972 Science 177 393 Google Scholar
[2]	Lifshitz E M, Pitaevskii L P 1980 Statistical Physics Part 2: Theory of the Condensed State (New York: Pergamon Press) p1
[3]	Klitzing K V, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494 Google Scholar
[4]	Tsui D C, Stormer H L, Gossard A C 1982 Phys. Rev. Lett. 48 1559 Google Scholar
[5]	Bednorz J G, Müler K A 1986 Z. Phys. B. 64 189 Google Scholar
[6]	Laughlin R B 1983 Phys. Rev. Lett. 50 1395 Google Scholar
[7]	Broholm C, Cava R J, Kivelson S A, Nocera D G, Norman M R, Senthil T 2020 Science 367 eaay0668 Google Scholar
[8]	Keimer B, Kivelson S A, Norman M R, Uchida S, Zaanen J 2015 Nature 518 179 Google Scholar
[9]	Wen X G 1990 Int. J. Mod. Phys. B 4 239 Google Scholar
[10]	Zeng B, Chen X, Zhou D L, Wen X G 2019 Quantum Information Meets Quantum Matter: From Quantum Entanglement to Topological Phases of Many-Body Systems (New York: Springer) p1
[11]	Semeghini G, Levine H, Keesling A, Ebadi S, Wang T T, Bluvstein D, Verresen R, Pichler H, Kalinowski M, Samajdar R, Omran A, Sachdev S, Vishwanath A, Greiner M, Vuletić V, Lukin M D 2021 Science 374 1242 Google Scholar
[12]	Satzinger K J, Liu Y J, Smith A, Knapp C, Newman M, Jones C, Chen Z, Quintana C, Mi X, Dunsworth A, Gidney C, Aleiner I, Arute F, Arya K, Atalaya J, Babbush R, Bardin J C, Barends R, Basso J, Bengtsson A, Bilmes A, Broughton M, Buckley B B, Buell D A, Burkett B, Bushnell N, Chiaro B, Collins R, Courtney W, Demura S, Derk A R, Eppens D, Erickson C, Faoro L, Farhi E, Fowler A G, Foxen B, Giustina M, Greene A, Gross J A, Harrigan M P, Harrington S D, Hilton J, Hong S, Huang T, Huggins W J, Ioffe L B, Isakov S V, Jeffrey E, Jiang Z, Kafri D, Kechedzhi K, Khattar T, Kim S, Klimov P V, Korotkov A N, Kostritsa F, Landhuis D, Laptev P, Locharla A, Lucero E, Martin O, McClean J R, McEwen M, Miao K C, Mohseni M, Montazeri S, Mruczkiewicz W, Mutus J, Naaman O, Neeley M, Neill C, Niu M Y, O'Brien T E, Opremcak A, Pató B, Petukhov A, Rubin N C, Sank D, Shvarts V, Strain D, Szalay M, Villalonga B, White T C, Yao Z, Yeh P, Yoo J, Zalcman A, Neven H, Boixo S, Megrant A, Chen Y, Kelly J, Smelyanskiy V, Kitaev A, Knap M, Pollmann F, Roushan P 2021 Science 374 1237 Google Scholar
[13]	Cai J, Anderson E, Wang C, Zhang X, Liu X, Holtzmann W, Zhang Y, Fan F, Taniguchi T, Watanabe K, Ran Y, Cao T, Fu L, Xiao D, Yao W, Xu X 2023 Nature 622 63 Google Scholar
[14]	Zeng Y, Xia Z, Kang K, Zhu J, Knüppel P, Vaswani C, Watanabe K, Taniguchi T, Mak K F, Shan J 2023 Nature 622 69 Google Scholar
[15]	Park H, Cai J, Anderson E, Zhang Y, Zhu J, Liu X, Wang C, Holtzmann W, Hu C, Liu Z, Taniguchi T, Watanabe K, Chu J H, Cao T, Fu L, Yao W, Chang C Z, Cobden D, Xiao D, Xu X 2023 Nature 622 74 Google Scholar
[16]	Xu F, Sun Z, Jia T, Liu C, Xu C, Li C, Gu Y, Watanabe K, Taniguchi T, Tong B, Jia J, Shi Z, Jiang S, Zhang Y, Liu X, Li T 2023 Phys. Rev. X 13 031037 Google Scholar
[17]	Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045 Google Scholar
[18]	Wen J, Yu S L, Li S, Yu W, Li J X 2019 npj Quantum Mater. 4 1 Google Scholar
[19]	Shimokawa T, Watanabe K, Kawamura H 2015 Phys. Rev. B 92 134407 Google Scholar
[20]	Ma Z, Wang J, Dong Z Y, Zhang J, Li S, Zheng S H, Yu Y, Wang W, Che L, Ran K, Bao S, Cai Z, Čermák P, Schneidewind A, Yano S, Gardner J S, Lu X, Yu S L, Liu J M, Li S, Li J X, Wen J 2018 Phys. Rev. Lett. 120 087201 Google Scholar
[21]	Kasahara Y, Ohnishi T, Mizukami Y, Tanaka O, Ma S, Sugii K, Kurita N, Tanaka H, Nasu J, Motome Y, Shibauchi T, Matsuda Y 2018 Nature 559 227 Google Scholar
[22]	Scholl P, Schuler M, Williams H J, Eberharter A A, Barredo D, Schymik K N, Lienhard V, Henry L P, Lang T C, Lahaye T, Läuchli A M, Browaeys A 2021 Nature 595 233 Google Scholar
[23]	Ebadi S, Wang T T, Levine H, Keesling A, Semeghini G, Omran A, Bluvstein D, Samajdar R, Pichler H, Ho W W, Choi S, Sachdev S, Greiner M, Vuletić V, Lukin M D 2021 Nature 595 227 Google Scholar
[24]	Cao Y, Fatemi V, Demir A, Fang S, Tomarken S L, Luo J Y, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E, Ashoori R C, Jarillo-Herrero P 2018 Nature 556 80 Google Scholar
[25]	Tang E, Mei J W, Wen X G 2011 Phys. Rev. Lett. 106 236802 Google Scholar
[26]	Neupert T, Santos L, Chamon C, Mudry C 2011 Phys. Rev. Lett. 106 236804 Google Scholar
[27]	Kitaev A 2006 Ann. Phys. 321 2 Google Scholar
[28]	Ghiotto A, Shih E M, Pereira G S S G, Rhodes D A, Kim B, Zang J, Millis A J, Watanabe K, Taniguchi T, Hone J C, Wang L, Dean C R, Pasupathy A N 2021 Nature 597 345 Google Scholar
[29]	Pan H, Wu F, Sarma S D 2020 Phys. Rev. Res. 2 033087 Google Scholar

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