受限一维无自旋费米子系统的性质研究

王婵娟; 陈阿海; 高先龙

doi:10.7498/aps.61.127501

摘要

本文借助于一维自旋1/2-XXZ模型的Bethe-ansatz精确解, 利用局域密度近似(LDA), 讨论了谐振势中一维无自旋费米子的密度分布, 得出了-u相图(这里的为无量纲的粒子数密度变量u为相互作用强度)对相图的分析表明, 随着原子密度和近邻相互作用的变化, 系统出现五个不同的混合量子相通过对热力学硬度S的计算, 发现其可作为体系的序参量, 其奇异点可用以度量受限体系中量子相变的发生

关键词:

According to the exact analytical Bethe-ansatz solution of the one-dimensional spin-1/2 XXZ model, we perform a numerical study of one-dimensional spinless fermions in an optical lattice in the presence of harmonic potential by using a local density approximation. We study the density profile, and obtain the -u phase diagram (here =NfV2/t is the characteristic dimensionless density and u=V/t is the interaction strength scaled in units of the hopping parameter t). With the increases of particle density and nearest-neighbour interaction, the system undergoes five different quantum phases. Through calculating the thermodynamic stiffness S, we find that it can be used as an order parameter. Its singular points can measure the quantum phase transitions in such a confined system.

Keywords:

作者及机构信息

1.
浙江师范大学物理系, 金华 321004

基金项目: 国家自然科学基金(批准号: 10974181, 11174253)和浙江省自然科学基金(批准号: R6110175) 资助的课题.

Authors and contacts

1.
Department of Physics, Zhejiang Normal University, Jinhua 321004, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 10974181, 11174253), and the Natural Science Foundation of Zhejiang Province (Grant No. R6110175).

参考文献

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[2]	Loh E Y, Campbell D K 1998 Synth. Met. 27A 499
[3]	Schulz H J 1990 Phys. Rev. Lett. 64 2831
[4]	Stafford C A, Millis A J, Shastry B S 1990 Phys. Rev. B 43 13660
[5]	Fye R M, Martins M J, Scalapino D J, Wagner J, Hanke W 1991 Phys. Rev. B 44 6909
[6]	Giamarchi T, Millis A J 1992 Phys. Rev. B 46 9325
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[9]	Song J, Cao Z L 2005 Acta Phys. Sin. 54 696 (in Chinese)[宋军, 曹卓良 2005 物理学报 54 696]
[10]	Wei B B, Cao J P, Gu S J, Lin H Q arXiv:0807.2154v1.
[11]	Guan L, Chen S, Wang Y, Ma Z Q 2009 Phys. Rev. Lett. 102 160402
[12]	Gao X L 2010 Phys. Rev. B 81 104306
[13]	Zhang S J, Jiang J J, Liu Y J 2008 Acta Phys. Sin. 57 531 (in Chinese)[张松俊, 蒋建军, 刘拥军 2008 物理学报 57 531]
[14]	Jordan P, Wigner E 1928 Z. Phys. 47 631 Yang C N, Yang C P 1966 Phys. Rev. 150 321
[15]	Bergkvist S, Henelius P, Rosengren A 2004 Phys. Rev. A 70 053601
[16]	Lima N A, Oliveira L N, Cappelle K 2002 Europhys. Lett. 60 601
[17]	Lima N A, Silva M F, Oliveira L N, Cappelle K 2003 Phys. Rev. Lett. 90 146402
[18]	Gao X L Rizzi M, Polini M, Fazio R, Tosi M P, Campo Jr. V L, Capelle K 2007 Phys. Rev. Lett. 98 030404
[19]	Gao X L Polini M, Tosi M P, Campo V L, Capelle K, Rigol M 2007 Phys. Rev. B 73 165120
[20]	Alcaraz F C, Capelle K 2007 Phys. Rev. B 76 035109
[21]	Schenk S, Dzierzawa M, Schwab P, Eckern U 2008 Phys. Rev. B 78 165102
[22]	Gaudin M 1975 Phys. Rev. Lett. 26 1301
[23]	Bethe H Z 1931 Phys. 71 205
[24]	Kohn W, Sham L J 1965 Phys. Rev. 140 A 1133
[25]	Capelle K, Vignale G 2002 Phys. Rev. B 65 113106
[26]	Elliott H, Lieb, Wu F Y 1968 Phys. Rev. Lett. 20 1445
[27]	Peres N M R, Sacramento P D, Campbell D K, Carmelo J M P 1998 Phys. Rev. B 59 11
[28]	Gu S J 2010 Int. J Mod. Phys. B 24 4371 Hu J H, Wang J J, Gao X L, Okumura M, Igarashi R, Yamada S, Machida M 2010 Phys. Rev. B 82 014202
[29]	Scarola V W, Pollet L, Oitmaa J, Troyer M 2009 Phys. Rev. Lett. 102 135302, 135305

施引文献

[1]	Pierre F, Maldague 1997 Phys. Rev. B 16 2437
[2]	Loh E Y, Campbell D K 1998 Synth. Met. 27A 499
[3]	Schulz H J 1990 Phys. Rev. Lett. 64 2831
[4]	Stafford C A, Millis A J, Shastry B S 1990 Phys. Rev. B 43 13660
[5]	Fye R M, Martins M J, Scalapino D J, Wagner J, Hanke W 1991 Phys. Rev. B 44 6909
[6]	Giamarchi T, Millis A J 1992 Phys. Rev. B 46 9325
[7]	Carmelo J M P, Horsch P 1992 Phys. Rev. Lett. 68 871 Carmelo J M P, Horsch P, Ovchinnikov A A 1992 Phys. Rev. B 46 14728
[8]	Wang Y H, Xia Y 2009 Acta Phys. Sin. 58 7479 (in Chinese)[王彦辉, 夏云 2009 物理学报 58 7479]
[9]	Song J, Cao Z L 2005 Acta Phys. Sin. 54 696 (in Chinese)[宋军, 曹卓良 2005 物理学报 54 696]
[10]	Wei B B, Cao J P, Gu S J, Lin H Q arXiv:0807.2154v1.
[11]	Guan L, Chen S, Wang Y, Ma Z Q 2009 Phys. Rev. Lett. 102 160402
[12]	Gao X L 2010 Phys. Rev. B 81 104306
[13]	Zhang S J, Jiang J J, Liu Y J 2008 Acta Phys. Sin. 57 531 (in Chinese)[张松俊, 蒋建军, 刘拥军 2008 物理学报 57 531]
[14]	Jordan P, Wigner E 1928 Z. Phys. 47 631 Yang C N, Yang C P 1966 Phys. Rev. 150 321
[15]	Bergkvist S, Henelius P, Rosengren A 2004 Phys. Rev. A 70 053601
[16]	Lima N A, Oliveira L N, Cappelle K 2002 Europhys. Lett. 60 601
[17]	Lima N A, Silva M F, Oliveira L N, Cappelle K 2003 Phys. Rev. Lett. 90 146402
[18]	Gao X L Rizzi M, Polini M, Fazio R, Tosi M P, Campo Jr. V L, Capelle K 2007 Phys. Rev. Lett. 98 030404
[19]	Gao X L Polini M, Tosi M P, Campo V L, Capelle K, Rigol M 2007 Phys. Rev. B 73 165120
[20]	Alcaraz F C, Capelle K 2007 Phys. Rev. B 76 035109
[21]	Schenk S, Dzierzawa M, Schwab P, Eckern U 2008 Phys. Rev. B 78 165102
[22]	Gaudin M 1975 Phys. Rev. Lett. 26 1301
[23]	Bethe H Z 1931 Phys. 71 205
[24]	Kohn W, Sham L J 1965 Phys. Rev. 140 A 1133
[25]	Capelle K, Vignale G 2002 Phys. Rev. B 65 113106
[26]	Elliott H, Lieb, Wu F Y 1968 Phys. Rev. Lett. 20 1445
[27]	Peres N M R, Sacramento P D, Campbell D K, Carmelo J M P 1998 Phys. Rev. B 59 11
[28]	Gu S J 2010 Int. J Mod. Phys. B 24 4371 Hu J H, Wang J J, Gao X L, Okumura M, Igarashi R, Yamada S, Machida M 2010 Phys. Rev. B 82 014202
[29]	Scarola V W, Pollet L, Oitmaa J, Troyer M 2009 Phys. Rev. Lett. 102 135302, 135305

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