论文标题
$ j_1-j_2 $ heisenberg型号的光谱功能在三角晶格上
Spectral function of the $J_1-J_2$ Heisenberg model on the triangular lattice
论文作者
论文摘要
光谱探针，例如中子散射，对于表征量子多体系统和量子材料的特性的激发至关重要。物质最难以捉摸的阶段之一是量子自旋液体，即使在零温度下也没有远距离顺序，并且具有非平凡统计的宿主外来分数激发。这些阶段可能发生在沮丧的量子磁铁中，例如在三角形晶格上最近和下一个最新的邻居交换相互作用，即所谓的$ j_1-j_2 $模型。在这项工作中，我们使用该模型相图的三个不同阶段的大型矩阵产品状态模拟计算光谱函数，包括中间$ J_2/J_1 $的量子自旋液相。尽管有大量理论和实验研究，但此阶段的确切性质仍在争夺中，主要候选人是$ \ mathbb {z} _2 _2 $，一个间隙$ u（1）$ dirac和Spinon fermi Fermi表面量子液态。我们在Brillouin区域中心（$γ$点）附近发现了一个V形光谱，这是Spinon费米表面的关键特征，在先前的中子散射实验中观察到。但是，我们发现$γ$点附近的一个很小的差距，排除了这样的阶段。此外，我们在布里渊区边界（k点）的角落和布里渊区边界边缘（m点）的中间发现了局部无间隙激发，排除了间隙的$ \ mathbb {z} _2 _2 _2 $旋转液相。我们的结果表明，中间自旋液相是无间隙$ U（1）$ DIRAC自旋液体，并提供清晰的签名来检测未来的中子散射实验中的这一阶段。
Spectral probes, such as neutron scattering, are crucial for characterizing excitations in quantum many-body systems and the properties of quantum materials. Among the most elusive phases of matter are quantum spin liquids, which have no long-range order even at zero temperature and host exotic fractionalized excitations with non-trivial statistics. These phases can occur in frustrated quantum magnets, such as the paradigmatic Heisenberg model with nearest and next-nearest neighbor exchange interactions on the triangular lattice, the so-called $J_1-J_2$ model. In this work, we compute the spectral function using large scale matrix product state simulations across the three different phases of this model's phase diagram, including a quantum spin liquid phase at intermediate $J_2/J_1$. Despite a plethora of theoretical and experimental studies, the exact nature of this phase is still contested, with the dominant candidates being a gapped $\mathbb{Z}_2$, a gapless $U(1)$ Dirac, and a spinon Fermi surface quantum spin liquid state. We find a V-shaped spectrum near the center of the Brillouin zone ($Γ$ point), a key signature of a spinon Fermi surface, observed in prior neutron scattering experiments. However, we find a small gap near the $Γ$ point, ruling out such a phase. Furthermore, we find localized gapless excitations at the corner of the Brillouin zone boundary (K point) and the middle of the edge of the Brillouin zone boundary (M point), ruling out the gapped $\mathbb{Z}_2$ spin liquid phase. Our results imply that the intermediate spin liquid phase is a gapless $U(1)$ Dirac spin liquid, and provide clear signatures to detect this phase in future neutron scattering experiments.
