论文标题
哈伯德模型在蜂窝晶格上的半摩托绝缘子量子相变
The Semimetal-Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice
论文作者
论文摘要
我们利用了最新的大型杂种蒙特卡洛算法的改善，以对具有现场电子电子相互作用的六边形哈伯德模型中的单粒子间隙进行精确研究。经过仔细控制猪肉误差的分析，热力学极限和有限大小的缩放，我们发现$ u_c/κ= 3.834（14）$的关键耦合以及关键指数$zν= 1.185（43）$。在假设这对应于预期的抗铁磁莫特过渡的假设下，我们还能够为订单参数的关键指数提供初步估计$β= 1.095（37）$。鉴于$ su（2）$ gross-neveu或Hairal Heisenberg，普遍性班级，我们考虑了我们的发现。我们还讨论了混合蒙特卡洛算法的计算缩放，以及我们的工作可能扩展到碳纳米管，富勒伦和拓扑绝缘子。
We take advantage of recent improvements in the grand canonical Hybrid Monte Carlo algorithm, to perform a precision study of the single-particle gap in the hexagonal Hubbard model, with on-site electron-electron interactions. After carefully controlled analyses of the Trotter error, the thermodynamic limit, and finite-size scaling with inverse temperature, we find a critical coupling of $U_c/κ=3.834(14)$ and the critical exponent $zν=1.185(43)$. Under the assumption that this corresponds to the expected anti-ferromagnetic Mott transition, we are also able to provide a preliminary estimate $β=1.095(37)$ for the critical exponent of the order parameter. We consider our findings in view of the $SU(2)$ Gross-Neveu, or chiral Heisenberg, universality class. We also discuss the computational scaling of the Hybrid Monte Carlo algorithm, and possible extensions of our work to carbon nanotubes, fullerenes, and topological insulators.
