美国物理学家索利斯（David J.Thouless）、霍尔丹（F.Duncan M.Haldane）、科斯德里茨（J.Michael Kosterlitz）因“关于拓扑相变和物质拓扑相的理论发现”获得2016年度诺贝尔物理学奖。介绍了这3位诺贝尔物理学奖获得者的学术经历，并从拓扑与拓扑相变、量子霍尔效应中的拓扑、1维量子反铁磁与对称性保护的拓扑态等方面探析拓扑相变和物质拓扑相理论发现的科学意义。
The 2016 Nobel Prize in Physics was awarded to David J. Thouless, F. Duncan M. Haldane and J. Michael Kosterlitz for their theoretical discoveries of topological phase transition and topological phases of matter. This article introduces their research experiences and describes the awarded achievements, as well as the scientific background and later development, from the aspects of topology and topological phase transitions, topology in quantum Hall effect, one dimensional antiferrom agnet and symmetry-protected topological states.
[1] Nobel Media AB 2016. Press release:The Nobel Prize in Physics 2016[EB/OL].[2016-11-16]. http://www.nobelprize.org/nobel_prizes/physics/laureates/2016/.
[2] Nobel Media AB 2016. The Nobel Prize in Physics 2016-popular infor-mation[EB/OL].[2016-11-16]. http://www.nobelprize.org/nobel_prizes/physics/laureates/2016/popular.html.
[3] Nobel Media AB 2016. The Nobel Prize in Physics 2016-advanced in-formation[EB/OL].[2016-11-16]. http://www.nobelprize.org/nobel_priz-es/physics/laureates/2016/advanced.html.
[4] Mermin N D, Wagner H. Absence of ferromagnetism or antiferromagnet-ism in one-or two-dimensional isotropic Heisenberg models[J]. Physi-cal Review Letters, 1966, 17:1133-1136.
[5] Hohenberg P C. Existence of long-range order in one and two dimen-sions[J]. Physical Review, 1967, 158:383-386.
[6] Wegner F. Spin-ordering in a planar classical Heisenberg model[J]. Zeitschrift für Physik, 1967, 206(5):465-470.
[7] Kosterlitz J M, Thouless D J. Long range order and metastability in two dimensional solids and superfluids[J]. Journal of Physics C:Solid State Physics, 1972, 5(11):L124-L126.
[8] Kosterlitz J M, Thouless D J. Ordering, metastability and phase transi-tions in two-dimensional systems[J]. Journal of Physics C:Solid State Physics, 1873, 6(7):1181-1203.
[9] Kosterlitz J M. The critical properties of the two-dimensional xymodel[J]. Journal of Physics C:Solid State Physics, 1974, 7(6):1046-1060.
[10] Hadzibabic Z, Krüger P, Cheneau M, et al. Berezinskii-KosterlitzThouless crossover in a trappedatomic gas[J]. Nature, 2006, 441(7097):1118-1121.
[11] Media AB 2014. Press release:The 1985 Nobel Prize in Physics[EB/OL].[2016-11-16]. http://www.nobelprize.org/nobel_prizes/physics/lau-reates/1985/press.html.
[12] Thouless D J, Kohmoto M, Nightingale M P, et al. Quantized Hall con-ductance in a two-dimensional periodic potential[J]. Physical Review Letters, 1982, 49(6):405-408.
[13] Niu Q, Thouless D J, Wu Y. Quantized hall conductance as a topologi-cal invariant[J]. Physical Review B, 1985, 31(6):3372-3377.
[14] Aidelsburger M, Lohse M, Schweizer C, et al. Measuring the Chern number of hofstadter bands with ultracold bosonic atoms[J]. Nature Physics, 2015, 11(2):162-166.
[15] Haldane F D M. Model for a quantum Hall effect without Landau lev-els:Condensed-Matter realization of the "parity anomaly"[J]. Physical Review Letters, 1988, 61(18):2015-2018.
[16] Jotzu G, Messer M, Desbuquois R, et al. Experimental realization of the topological Haldane model with ultracold fermions[J]. Nature, 2014, 515(7526):237-240.
[17] Kane C L, Mele E J. Quantum spin Hall effect in graphene[J]. Physi-cal Review Letters, 2005, 95:226801.
[18] Bernevig B A, Zhang S C. Quantum spin Hall effect[J]. Physical Re-view Letters, 2006, 96:106802.
[19] Konig M, et al. Quantum spin Hall insulator state in HgTe quantum wells[J]. Science, 2007, 318(5851):766-770.
[20] Chang C Z, Zhang J, Feng X, et al. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator[J]. Science, 2013, 340(6129):167-170.
[21] Haldane F D M. Continuum dynamics of the 1-D Heisenberg antiferro-magnet:Identification with the O(3) nonlinear sigma model[J]. Physics Letters A, 1983, 93(9):464-468.
[22] Haldane F D M. Nonlinear field theory of large-spin Heisenberg anti-ferromagnets:Semiclassically quantized solitons of the one-dimension-al easy-axis néel state[J]. Physical Review Letters, 1983, 50(15):1153-1156.
[23] Kenzelmann M, Cowley R A, Buyers W J L, et al. Properties of Hal-dane excitations and multiparticle states in the antiferromagnetic spin-1 chain compound CsNiCl3[J]. Physical Review B, 2002, 66(2):024407.
