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摘要: 如何理解棋盘晶格中的强关联电子现象是一个值得深入研究的问题．在阻挫系统中，量子蒙特卡罗模拟通常会遇到符号问题．我们采用约束路径量子蒙特卡罗方法，有效地避开符号问题，研究了定义在掺杂棋盘晶格Hubbard模型中的超导配对关联．我们发现
$ d $ 波对称性的超导配对关联函数优于其他对称性，$ d $ 波配对关联函数随着次近邻跃迁强度$ {t}' $ 的减小而增大，随着库仑相互作用的增加而增大．研究结果为进一步理解超导体中的关联效应及其超导配对机制提供了有价值的参考，也为理解阻挫和超导的关系提供了思路．Abstract: How to understand strong correlated electrons states in a checkerboard lattice is an interesting problem. In frustrated systems, quantum Monte Carlo simulation often suffers the sign problem. We use the constrained path quantum Monte Carlo method which could effectively avoid the sign problem, and study the superconducting pairing correlation in doped Hubbard model on a checkerboard lattice. We find that the superconducting pairing correlation function with d-wave symmetry dominates over other symmetries, and the d-wave pairing correlation function increases with next-nearest neighbor hopping strength t ' decreases, and increases when the coulomb interaction increases. Our results provide some valid points for further theoretical research on the correlation effect and superconductivity in superconductors, also provide ideas for understanding the relationship between frustration and superconductivity.-
Key words:
- checkerboard lattice /
- superconductivity /
- CPQMC /
- pairing symmetry
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图 2 在晶格尺寸
$ L=12 $ ，库仑相互作用$ U=4.0 $ ，电子浓度$ \langle n\rangle =0.875 $ 情况下，(a)$ {t}'=0.50 $ 、(b)$ {t}'=0.75 $ 、(c)$ {t}'=1.00 $ 和(d)$ {t}'=1.20 $ ，不同的次近邻跃迁强度$ t' $ 的配对关联函数$ {C}_{\alpha } $ 随距离$ \mathrm{r}/\mathrm{a} $ 的变化关系．
图 3 在晶格尺寸
$ L=12 $ , 库仑相互作用$ U=4.0 $ ，电子浓度$ \langle n\rangle =0.875 $ 的情况下, (a)为不同的次近邻跃迁强度$ t' $ 的对$ d $ 波配对关联函数$ {C}_{\alpha } $ 随距离$ \mathrm{r}/\mathrm{a} $ 的变化关系，$ t'=\mathrm{0.50,0.75,1.00,1.20,1.50} $ , (b)图为vertex函数随距离$ \mathrm{r}/\mathrm{a} $ 的变化关系．
图 4 在晶格尺寸
$ L=12 $ , 次近邻跃迁强度$ t'=1.50 $ ，电子浓度$ \langle n\rangle =0.875 $ 的情况下, 不同的库仑相互作用$ U$ = 3.0, 4.0, 5.0, 6.0，(a)图为d波配对关联函数$ {C}_{\alpha } $ 随距离$ \mathrm{r}/\mathrm{a} $ 的变化关系, (b)图为vertex函数随距离$ \mathrm{r}/\mathrm{a} $ 的变化关系． -
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