双层哈伯德模型中激子态的数值研究

Numerical Study of Exciton Condensation in the Bilayer Hubbard Model

摘要: 本文采用约束路径量子蒙特卡罗方法系统地探讨了双层哈伯德模型中的激子态特性。计算结果表明，当空穴和电子掺杂浓度低于0.08时，由层间单粒子隧穿强度表征的局域激子态被层间库仑相互作用V增强，且随着掺杂浓度的减小增强效应逐渐变强，而当空穴和电子掺杂浓度高于0.08时，局域激子态却被V减弱。该结果与已发表的有限温度结果存在重要的差异。进一步的分析发现在整个掺杂区间，激子的长程空间关联函数随着V的增加而减小，表明研究的双层哈伯德模型中不存在激子序参量的长程序，即激子凝聚态。此外，层间库仑相互作用V对格点磁矩的影响很小。

Abstract: This work investigates the exciton property of the bilayer Hubbard model by using the con-strained-path Monte Carlo method. The calculated results show that when the doping density is lower than 0.08, the local exciton characterized by interlayer single particle tunneling is enhanced by the interlayer Coulomb interaction V, and the enhancement becomes stronger with decreasing the doping density. However, when the doping density is higher than 0.08, the local exciton is sup- pressed by V. This result exhibits significant differences from the published results at finite temperatures. Further analysis shows that the long-range exciton correlation function is reduced with increasing V, demonstrating that there does not exist exciton condensation in the studied model. In addition, the interlayer Coulomb interaction V is shown to have a rather weak effect on local magnetic moment.