AI 中文总结
研究三角晶格上\(J_1-J_2\)海森堡模型在小磁场下的基态相图，用变分蒙特卡罗方法，在特定参数区域研究，发现\(J_2/J_1 \lesssim 1/6\)的转变，以及\(J_2/J_1 = 1/8\)附近单极子相稳定存在并获相关边界。
AI 中文摘要
我们使用变分蒙特卡罗方法研究了在外部塞曼场\(H\)下三角晶格上\(J_1-J_2\)海森堡模型的基态相图。我们在\(0 \le J_2/J_1 \le 0.2\)和\(0 \le H/J_1 \le 2\)的区域内进行研究，以评估在零磁场下\(J_2/J_1 = 1/8\)时检测到的（假定的）自旋液体相的命运。针对几个候选态提出了简单的变分波函数，并在大团簇上比较它们的能量以获得相图。对于\(J_2/J_1 \lesssim 1/6\)，如自旋波理论所预测的，得到了从无隙“Y”相到有隙“上-上-下”相的连续转变。最重要的是，在\(J_2/J_1 = 1/8\)附近，对于小塞曼场，单极子凝聚体（\(H = 0\)时自旋液体的无隙规范激发）在相图的一个显著区域中稳定存在。这里存在有限的标量手征性，而未检测到横向磁序。通过包括低能自旋涨落的自洽随机相位近似的场论方法证实了单极子相的稳定性。还在没有自由参数的情况下得到了单极子相和“Y”相之间的边界。
英文摘要
We investigate the ground-state phase diagram of the $J_1{-}J_2$ Heisenberg model on the triangular lattice under an external Zeeman field $H$ by using the variational Monte Carlo approach. We span a region with $0 \le J_2/J_1 \le 0.2$ and $0 \le H/J_1 \le 2$, to assess the fate of the (putative) spin-liquid phase that has been detected for $J_2/J_1=1/8$ at zero magnetic field. Simple variational ansatze are proposed for a few candidate states, and their energetics are compared on large clusters to obtain the phase diagram. For $J_2/J_1 \lesssim 1/6$, a continuous transition from a gapless "Y'' phase to a gapped "up-up-down'' phase is obtained, as predicted by spin-wave theory. Most importantly, around $J_2/J_1=1/8$, a condensate of monopoles (which are gapless gauge excitations of the spin liquid at $H=0$) is stabilized in a significant region of the phase diagram, for small Zeeman fields. Here, a finite scalar chirality is present, while no transverse magnetic order is detected. The stability of the monopole phase is confirmed by a field-theory approach that includes a self-consistent random-phase approximation of the low-lying spin fluctuations. The boundary between the monopole and "Y'' phases is also obtained with no free parameters.
Comments13 pages, 10 figures
