Understanding many-body physics in one dimension from the Lieb-Liniger model

doi:10.1088/1674-1056/24/5/050311

中国物理B ›› 2015, Vol. 24 ›› Issue (5): 50311-050311.doi: 10.1088/1674-1056/24/5/050311

所属专题： TOPICAL REVIEW — Precision measurement and cold matters

• TOPICAL REVIEW—Precision measurement and cold matters • 上一篇下一篇

Understanding many-body physics in one dimension from the Lieb-Liniger model

姜玉铸^{a b}, 陈洋洋^{a b}, 管习文^{a b}

a State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China;
b Center for Cold Atom Physics, Chinese Academy of Sciences, Wuhan 430071, China

收稿日期:2015-01-13 修回日期:2015-02-22 发布日期:2015-05-25
基金资助:
Project supported by the National Basic Research Program of China (Grant No. 2012CB922101) and the National Natural Science Foundation of China (Grant Nos. 11374331 and 11304357).

Understanding many-body physics in one dimension from the Lieb-Liniger model

Jiang Yu-Zhu (姜玉铸)^{a b}, Chen Yang-Yang (陈洋洋)^{a b}, Guan Xi-Wen (管习文)^{a b}

a State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China;
b Center for Cold Atom Physics, Chinese Academy of Sciences, Wuhan 430071, China

Received:2015-01-13 Revised:2015-02-22 Published:2015-05-25
Contact: Guan Xi-Wen E-mail:xwe105@wipm.ac.cn
About author:2015-4-17
Supported by:
Project supported by the National Basic Research Program of China (Grant No. 2012CB922101) and the National Natural Science Foundation of China (Grant Nos. 11374331 and 11304357).

摘要/Abstract

摘要：

This article presents an elementary introduction on various aspects of the prototypical integrable model the Lieb- Liniger Bose gas ranging from the cooperative to the collective features of many-body phenomena. In 1963, Lieb and Liniger first solved this quantum field theory many-body problem using Bethe's hypothesis, i.e., a particular form of wavefunction introduced by Bethe in solving the one-dimensional Heisenberg model in 1931. Despite the Lieb-Liniger model is arguably the simplest exactly solvable model, it exhibits rich quantum many-body physics in terms of the aspects of mathematical integrability and physical universality. Moreover, the Yang-Yang grand canonical ensemble description for the model provides us with a deep understanding of quantum statistics, thermodynamics, and quantum critical phenomena at the many-body physical level. Recently, such fundamental physics of this exactly solved model has been attracting growing interest in experiments. Since 2004, there have been more than 20 experimental papers that reported novel observations of different physical aspects of the Lieb-Liniger model in the laboratory. So far the observed results are in excellent agreement with results obtained using the analysis of this simplest exactly solved model. Those experimental observations reveal the unique beauty of integrability.

关键词: many-body physics, Lieb-Liniger model

Abstract:

Key words: many-body physics, Lieb-Liniger model

中图分类号: (Degenerate Fermi gases)

03.75.Ss

71.10.Pm (Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.)) 02.30.Ik (Integrable systems)

姜玉铸, 陈洋洋, 管习文. Understanding many-body physics in one dimension from the Lieb-Liniger model[J]. 中国物理B, 2015, 24(5): 50311-050311.

Jiang Yu-Zhu (姜玉铸), Chen Yang-Yang (陈洋洋), Guan Xi-Wen (管习文). Understanding many-body physics in one dimension from the Lieb-Liniger model[J]. Chin. Phys. B, 2015, 24(5): 50311-050311.

参考文献 98

[1]	Bethe H 1931 Z. Physik 71 205
[2]	Lieb E H and Liniger W 1963 Phys. Rev. 130 1605
[3]	Yang C N and Yang C P 1969 J. Math. Phys. 10 1115
[4]	Yang C N 1967 Phys. Rev. Lett. 19 1312
[5]	Baxter R J 1972 Ann. Phys. 70 193
[6]	Baxter R J 1972 Ann. Phys. 70 323
[7]	Gaudin M 1967 Phys. Lett. A 24 55
[8]	Baxter R J 1982 Exactly Solved Models in Statistical Mechanics (London: Academic Press)
[9]	Yang C N 1983 Selected Papers 1945-1980 W. H. Freeman and Company
[10]	Yang C N 2013 Selected Papers II World Scientific
[11]	Korepin V E, Izergin A G and Bogoliubov N M 1993 Quantum Inverse Scattering Method and Correlation Functions (Cambridge: Cambridge University Press)
[12]	Takahashi M 1999 Thermodynamics of One-Dimensional Solvable Models (Cambridge: Cambridge University Press)
[13]	Essler F H L, Frahm H, Ghmann F, Klmper A and Korepin V E 2005 The One-Dimensional Hubbard Model (Cambridge: Cambridge University Press)
[14]	Sutherland B 2004 Beautiful Models (Singapore: World Scientific)
[15]	Gaudin M 2014 The Bethe Wavefunction (Cambridge: Cambridge University Press)
[16]	Olshanii M 1998 Phys. Rev. Lett. 81 938
[17]	Olshanii M and Dunjko V 2003 Phys. Rev. Lett. 91 090401
[18]	Dunjko V, Lorent V and Olshanii M 2001 Phys. Rev. Lett. 86 5413
[19]	Girardeau M, Nguyen H and Olshanii M 2004 Opt. Commun. 243 3
[20]	Gaudin M 1971 Phys. Rev. A 4 386
[21]	Iida T and Wadati M 2005 J. Phys. Soc. Jpn. 74 1724
[22]	Batchelor M T, Guan X W and Mcguire J B 2004 J. Phys. A 37 L497
[23]	Bortz M private communications
[24]	Paredes P 2004 Nature 429 277
[25]	Kinoshita T, Wenger T and Weiss D S 2004 Science 305 1125
[26]	Guan XWand BatchelorMT 2011 J. Phys. A: Math. Theor. 44 102001
[27]	Guan L M private communications
[28]	Panfil M and Caux J S 2014 Phys. Rev. A 89 033605
[29]	Ristivojevic Z 2014 Phys. Rev. Lett. 113 015301
[30]	Astrakharchik G E, Boronat J, Casulleras and Giorgini S 2005 Phys. Rev. Lett. 95 190407
[31]	BatchelorMT, Bortz M, Guan XWand Oelkers N 2005 J. Stat. Mech.: Theory Exp. L10001
[32]	Chen S, Guan L, Yin X, Hao Y and Guan X W 2010 Phys. Rev. A 81 031609
[33]	Panfil M, Nardis J D and Caux J S 2013 Phys. Rev. Lett. 110 125302
[34]	Kormos M, Mussardo G and Trombettoni A 2011 Phys. Rev. A 83 013617
[35]	GirardeauMD and Astrakharchik G E 2009 Phys. Rev. A 81 061601(R)
[36]	Giamarchi T 2004 Quantum Physics in One Dimension (Cambridge: Cambridge University Press)
[37]	CazalillaMA, Citro R, Giamarchi T, Orignac E and RigolM2011 Rev. Mod. Phys. 83 1405
[38]	Caux J S and Calabrese P 2006 Phys. Rev. A 74 031605
[39]	Panfil M and Caux J S 2014 Phys. Rev. A 89 033605
[40]	Belavin A A, Polyakov AMand Zamolodchikov A B 1984 Nucl. Phys. B 241 333
[41]	Guan X W, Batchelor M T and Lee C 2013 Rev. Mod. Phys. 85 1633
[42]	Gangardt D M and Shlyapnikov G V 2003 Phys. Rev. Lett. 90 010401
[43]	Kheruntsyan K V, Gangardt D M, Drummond P D and Shlyapnikov G V 2003 Phys. Rev. Lett. 91 040403
[44]	Batchelor M T and Guan X W 2007 Laser Phys. Lett. 4 77
[45]	Klumper A and Patu O I 2014 Phys. Rev. A 90 053626
[46]	Gangardt D M and Shlyapnikov G V 2003 Phys. Rev. Lett. 90 010401
[47]	Kheruntsyan K V, Gangardt D M, Drummond P D and Shlyapnikov G V 2003 Phys. Rev. Lett. 91 040403
[48]	Kheruntsyan K V, Gangardt D M, Drummond P D and Shlyapnikov G V 2005 Phys. Rev. A 71 053615
[49]	Tan S 2008 Ann. Phys. 323 2952
[50]	Tan S 2008 Ann. Phys. 323 2971
[51]	Tan S 2008 Ann. Phys. 323 2987
[52]	Chen Y Y, Jiang Y Z, Guan X W and Zhou Q 2014 Nat. Commun. 5 51040
[53]	Cazalilla M A 2003 Phys. Rev. A 67 053606
[54]	Guan X W, Batchelor M T and Takahashi M 2007 Phys. Rev. A 76 043617
[55]	Batchelor M T 2014 Int. J. Mod. Phys. B 28 1430010
[56]	Kinoshita T, Wenger T and Weiss D S 2005 Phys. Rev. Lett. 95 190406
[57]	Guarrera V, Muth D, Labouvle R, Vogler A, Barontlnl G, Flelschhauer M and Ott H 2012 Phys. Rev. A 86 021601
[58]	Armijo J, Jacqmin T, Kheruntsyan and Bouchoule 2010 Phys. Rev. Lett. 105 230402
[59]	Tolra B L, O'Hara K M, Huckans J H, Phillips W D, Rolston S L and Porto J V 2004 Phys. Rev. Lett. 92 190401
[60]	Haller E, Rabie M, Mark M J, Danzl J G, Hart R, Lauber K, Pupillo G and Ngerl H C 2011 Phys. Rev. Lett. 107 230404
[61]	Kuhnert M, Geiger R, Langen T, Gring M, Rauer B, Kitagawa T, Demler E, Smith D A and Schmiedmayer J 2013 Phys. Rev. Lett. 110 090405
[62]	van Amerongen A H, van Es J J P, Wicke P, Kheruntsyan K V and van Druten N J 2008 Phys. Rev. Lett. 100 090402
[63]	Vogler A, Labouvie R, Stubenrauch F, Barontini G, Guarrera V and Ott H 2013 Phys. Rev. A 88 031603
[64]	Haller E, Gustavss M, Mark M J, Danzl J G, Hart R, Pupillo G and Ngerl H C 2009 Science 325 1224
[65]	Jacqmin T, Armijo J, Berrada T, Kheruntsyan K V and Bouchoule I 2011 Phys. Rev. Lett. 106 230405
[66]	Esteve J, Trebbia J B, Schumm T, Aspect A, Westbrook C I and Bouchoule I 2006 Phys. Rev. Lett. 96 130403
[67]	Armijo J 2012 Phys. Rev. Lett. 108 225306
[68]	Karpiuk T, Deuar P, Bienias P, Witkowska E, Pawlowski K, Gajda M, Rzazewski K and Brewczyk M 2012 Phys. Rev. Lett. 109 205302
[69]	Fabbri N, Panfil M, Clment D, Fallani L, Inguscio M, Fort C and Caux J S 2014 arXiv:1406.2176v2 [cond-mat.quant-gas]
[70]	Kinoshita T, Wenger T and Weiss D S 2006 Nature 440 900
[71]	Hofferberth S, Lesanovsky I, Fischer B, Schumm T and Schmiedmayer J 2007 Nature 449 324
[72]	Ronzheimer J P 2013 Phys. Rev. Lett. 110 205301
[73]	The experiments are chosen for the most relative to the Lieb-Liniger model, and by no means exhaustive.
[74]	Langen T, Geiger R, Kuhnert M, Rauer B and Schmiedmayer J 2013 Nat. Phys. 9 640
[75]	Stimming H P, Mauser N J, Schmiedmayer J and Mazets I E 2010 Phys. Rev. Lett. 105 015301
[76]	Langen T, Erne S, Geiger R, Rauer B, Schweigler T, Kuhnert M, Rohringer W, Mazets I E, Gasenzer T and Schmiedmayer J 2014 arXiv:1411.7185v1 [cond-mat.quant-gas])
[77]	Witkowska E, Deuar P, Gajda M and Rzaewski K 2011 Phys. Rev. Lett. 106 135301
[78]	Jacqmin T, Fang B, Berrada T, Roscllde T and Bouchoule I 2012 Phys. Rev. A 86 043626
[79]	Haller E, Hart R, Mark M J, Danzl J G, Reichsllner L, Gustavsson M, Dalmonte M, Pupillo G and Ngerl H C 2010 Nature 466 597
[80]	Guan X W 2014 Int. J. Mod. Phys. B 28 1430015
[81]	Guan X W, Batchelor M T and Takahashi M 2007 Phys. Rev. A 76 043617
[82]	Rigol M, Dunjko V, Yurovsky V and Olshanii M 2007 Phys. Rev. Lett. 98 050405
[83]	Rigol M, Dunjko V and Olshanii M 2008 Nature 452 854
[84]	Kormos M, Chou Y Z and Imambekov A 2011 Phys. Rev. Lett. 107 230405
[85]	Cheianov V V, Smith H and ZvonarevMB 2006 J. Stat. Mech. : Theory Exp. P08015
[86]	Kormos M, Mussardo G and Trombettoni A 2009 Phys. Rev. Lett. 103 210404
[87]	Kormos M, Mussardo G and Trombettoni A 2010 Phys. Rev. A 81 043606
[88]	Kormos M, Mussardo G and Pozsgay B 2010 J. Stat. Mech.: Theory Exp. P05014
[89]	Caux J S and Essler F H L 2013 Phys. Rev. Lett. 110 257203
[90]	Nardis J, Wouters B, Brockmann M and Caux J S 2014 Phys. Rev. A. 89 033601
[91]	Goldstein G and Andrei N 2014 arXiv:1405.6365v1 [cond-mat.quantgas]
[92]	Goldstein G and Andrei N 2013 arXiv:1309.3471v1 [cond-mat.quantgas]
[93]	Lyer D and Andrei N 2012 Phys. Rev. Lett. 109 115304
[94]	Pozsgay B 2014 arXiv:1406.4613v2 [cond-mat.stat-mech]
[95]	Wouters B, Nardis J D, Brockmann M, Fioretto D, Rigol M and Caux J S 2014 Phys. Rev. Lett. 113 117202
[96]	Brockmann M, Wouters B, Fioretto D, Nardis J D, Vlijm R and C J S 2014 J. Stat. Mech. P12009
[97]	Pozsgay B, Mestyn M, Werner M A, Kormos M, Zarnd G and Takcs G 2014 Phys. Rev. Lett. 113 117203
[98]	Goldstein G and Andrei N 2014 arXiv:1405.4224v2 [cond-mat.quantgas]

Understanding many-body physics in one dimension from the Lieb-Liniger model

Understanding many-body physics in one dimension from the Lieb-Liniger model

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