AI 中文总结
该研究通过数值模拟发现蜂窝海森堡模型在子格选择性相互作用下存在扩展对称区域，并提出了Z2狄拉克自旋液体作为候选基态。
AI 中文摘要
受二维双层系统的启发，我们在蜂窝晶格上数值研究了反铁磁自旋-$1/2$ 海森堡模型，该模型具有最近邻交换耦合 $J_1$，以及仅作用于 B 子格位点的次近邻交换耦合 $J_2'$。利用无限投影纠缠对态（iPEPS）、圆柱体上的变分均匀矩阵乘积态以及精确对角化，我们发现了一个扩展的对称区域 $0.4\backsimeq J'_2/J_1\backsimeq0.6$，在该区域内，局域可观测量不显示磁性、价键或手性自旋序。在 $J'_2/J_1=0.5$ 处，PEPS 关联长度随键维数系统性地增长，且逆关联长度外推倾向于消失极限。我们还发现，各种可观测量随有限键维数诱导的关联长度呈代数标度，这表明存在一个无能隙的自旋液体基态。我们提出一个 $\mathbb{Z}_2$ 狄拉克自旋液体部分子态，其狄拉克点受平移、时间反演和三重旋转对称性保护，作为解释数值结果的有希望的候选态。我们还讨论了对称基态可能是一个具有小能隙的无特征、短程纠缠态的可能性。
英文摘要
Motivated by two-dimensional bilayer systems we numerically study an anti-ferromagnetic spin-$1/2$ Heisenberg model on the honeycomb lattice with a nearest-neighbour exchange coupling $J_1$, and a next-nearest-neighbour exchange coupling $J_2'$ for the B sublattice sites only. Using infinite Projected Entangled-Pair States (iPEPS), variational uniform matrix-product states on cylinders, and exact diagonalization, we find an extended symmetric regime $0.4\lesssim J'_2/J_1\lesssim0.6$, in which local observables show no magnetic, valence-bond, or chiral spin order. At $J'_2/J_1=0.5$, the PEPS correlation length grows systematically with bond dimension, and an inverse-correlation-length extrapolation favors a vanishing limit. We also find that various observables scale algebraically with the finite bond-dimension-induced correlation length, which points to a gapless spin liquid ground state. We propose a $\mathbb{Z}_2$ Dirac spin liquid parton state, with Dirac points that are protected by translation, time-reversal and three-fold rotation symmetry, as a promising candidate state to explain the numerical results. We also discuss the possibility that the symmetric ground state is a featureless, short-range entangled state with a small gap.
Comments20 pages, 22 figures
