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采用随机级数展开的量子蒙特卡罗方法研究二维硬核的玻色-赫伯德模型的热力学性质. 首先通过算符变换将模型映射成为二维反铁磁准海森伯模型. 变换后的模型比通常的海森伯模型多一项, 该项正比于系统的格点总数N, 对于大粒子数的系统, 该项使模拟耗时指数增加, 所以难以计算大粒子数系统.采用非局域操作循环更新后, 这个困难可以得到很好的解决, 可使粒子数总数增大到几千个.研究结果表明, 粒子数密度在00.5范围内增大时, 能量呈递减趋势, 并趋于某一定值, 随着正方晶格系统尺度增大, 能量也随之增大;正方晶格系统尺度一定时, 能量和磁化强度随着温度的升高而增大, 化学势的变化对能量和磁化强度没有影响, 能量随着正方晶格系统尺度增大而增大, 磁化强度却随之减小;正方晶格系统尺度一定时, 化学势的增大对比热没有影响, 随着温度的升高比热出现先增大后减小的趋势, 最后趋于某个值, 达到平衡, 而正方晶格系统尺度越大, 比热曲线增大部分的趋势越大, 减小部分的趋势也更明显, 参照朗道超流理论, 本文模拟的能量和比热曲线趋势与朗道二流体模型下He II的理论研究一致; 不同正方晶格系统尺度的影响不大, 均匀磁化率倒数在00.5(J/kB)的低温范围内有很小的波动, J为耦合能, kB为玻尔兹曼常数, 温度在0.5-2 (J/kB)的范围内, 均匀磁化率的倒数随着温度的升高而增大, 且曲线的趋势显示了一种类似近藤行为.In this paper, the stochastic series expansion quantum Monte Carlo method is employed to investigate the thermodynamic properties of hardcore Bose-Hubbard model in two-dimensional space. The two-dimensional hardcore Bose-Hubbard model can be mapped into the two-dimensional antiferromagnetic quasi-Heisenberg model under transform of bosonic operators. There is an additional term which is proportional to the total number of sites compared with real Heisenberg model and it is difficult for simulation. Using a nonlocal operator-loop update, it allows one to simulate thousands of sites. Our simulation results show that, first, energy decreases with the increase of density of particles in a range from 0 to 0.5, and finally approaches to a fixed value. Moreover, with the size of square lattice increasing, energy also increases. Second, when we fix the system size, energy and magnetization increase with temperature, but not with of chemical potential. When we increase the system size, energy increases, while, the magnetization decreases. Third, specific heat is independent of chemical potential, but it dramatically increases with temperature and approaches to a peak, then decreases slowly. According to Landau theory of superfluidity, the tends of curve for energy and specific heat fit the research of He II in the Landau two-fluid model. Fourth, different square lattice linear system sizes have a little influence on tiny differences to the reciprocal of uniform susceptibility. There are small fluctuations in a range from 0 to 0.5(J/kB), where J is the coupling energy, kB is the Boltzmann constant, but the reciprocal of uniform susceptibility increases with temperature increasing in a range from 0.5 to 2(J/kB). The tends of curve are similar to those of Kondo effect.
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Keywords:
- quantum Monte Carlo method /
- stochastic series expansions /
- hardcore Boson /
- Bose-Hubbard model
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[2] Anderson M H, Ensher J R, Mathews M R, Weiman C E, Cornell E A 1995 Science 269 198
[3] Jaksch D, Bruder C, Cirac J I, Gardiner C W, Zoller P 1998 Phys. Rev. Lett. 81 3108
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[26] Jiang Z T 2010 Chin. Phys. B 19 077307
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[1] Leggett A J 2001 Rev. Mod. Phys. 73 307
[2] Anderson M H, Ensher J R, Mathews M R, Weiman C E, Cornell E A 1995 Science 269 198
[3] Jaksch D, Bruder C, Cirac J I, Gardiner C W, Zoller P 1998 Phys. Rev. Lett. 81 3108
[4] Greiner M, Mandel O, Esslinger T, HaÉnsch T W, Bloch I 2002 Nature 415 39
[5] Pollet L, Prokof'ev N V, Svistunov B V, Troyer M 2009 Phys. Rev. Lett. 103 140402
[6] Bakr W S, Peng A, Tai M E, Ma R, Simon J, Gillen J I, Folling S, Pollet L, Greiner M 2010 Science 329 547
[7] Crepin F, Laflorencie N, Roux G, Simon P 2011 Phys. Rev. B 84 054517
[8] Laflorencie N, Mila F 2011 Phys. Rev. Lett. 107 037203
[9] Jordan J, Orús R, Vidal G 2009 Phys. Rev. B 79 174515
[10] Hen I, Rigol M 2009 Phys. Rev. B 80 134508
[11] Fisher M P A, Weichman P B, Grinstein G, Fisher D S 1989 Phys. Rev. B 40 546
[12] Beijing University Physics Department “Quantum Statistical Physics” 1987 Quantum Statistical Physics (Beijing: Beijing University Press) pp232--240 (in Chinese) [北京大学物理系量子统计物理学angle编写组 1987 量子统计物理学 (北京: 北京大学出版社) 第232---240页]
[13] Landau D P, Binder K 2008 A Guide to Monte Carlo Simulations in Statistical Physics (2nd Ed.) (Beijing: BookWorld Publications) pp277--312
[14] Zhao X W, Cheng X L, Zhang H 2010 Acta Phys. Sin. 59 482 (in Chinese) [赵杏文, 程新路, 张红 2010 59 482]
[15] Zhou L, Liu Z J, Yan W B, Mu Z J 2011 Chin. Phys. B 20 074205
[16] Dorneich A, Troyer M 2001 Phys. Rev. E 64 066701
[17] Sylijuasen O F, Sandvik A W 2002 Phys. Rev. E 66 046701
[18] Zyubin M V, Kashurnikov V A 2004 Phys. Rev. E 69 036701
[19] Kawashima N, Gubernatis J E, Evertz H G 1994 Phys. Rev. B 50 136
[20] Alet F, Wessel S, Troyer M 2005 Phys. Rev. E 71 036706
[21] Zhou Q, Li J B 2011 Journal of Guangxi University (Nat. Sci. Ed.) 36 334 (in Chinese) [周琼, 李晋斌 2011 广西大学学报 (自然科学版) 36 334]
[22] Wang Z C 2005 Thermodynamics and Statistical Physics (Beijing: Higher Education Press) pp248--286 (in Chinese) [汪志诚 2005 热力学统计物理 (北京: 高等教育出版社) 第 248---286页]
[23] Li Z Z 1985 Solid State Theory (Beijing: Higher Education Press) pp390--402 (in Chinese) [李中正1985固体理论 (北京: 高等教育出版社) 第390---402页]
[24] Bernardet K, Batrouni G G, Meunier J L, Schmid G, Troyer M, Dorneich A 2002 Phys. Rev. B 65 104519
[25] Feng D, Jin G J 2003 Condensed Matter Physics (Vol. 1) (Beijing: Higher Education Press) pp381--417 (in Chinese) [冯端, 金国钧 2003 凝聚态物理学(上卷) (北京:高等教育出版社) 第 387---417页]
[26] Jiang Z T 2010 Chin. Phys. B 19 077307
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