-
朗道费米液体理论和金兹堡-朗道相变理论是传统凝聚态物理两座重要的基石, 在处理BCS超导体和液氦超流体的形成机制等重要物理问题中取得了巨大成功. 然而, 以20世纪80年代量子霍尔效应和高温超导的发现为开端, 人们逐渐认识到, 对于一大类新的量子态, 比如分数量子霍尔态和量子自旋液体, 其性质超越了朗道费米液体理论和金兹堡-朗道相变理论. 拓扑序及其所具有的长程多体量子纠缠和分数化激发成为我们理解这些奇异量子态的关键概念. 在量子材料和量子模拟系统中设计并寻找具有拓扑序的物态、探测并操控其分数化激发是当代凝聚态物理重要的研究方向. 近期, 在里德伯原子体系、超导量子处理器和二维摩尔超晶格等具有高度可调控性的量子实验平台中, 拓扑序的量子模拟和操控得到了快速发展并取得了重要成果. 本文将简要论述拓扑序在传统凝聚态材料体系和量子模拟体系中最近的研究进展和挑战, 并对该领域未来可能的发展方向做出展望.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
[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
-
[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
计量
- 文章访问数: 2871
- PDF下载量: 187
- 被引次数: 0
下载:
