论文标题
$ J_1-J_2 $ HEISENBERG模型中的无间隙旋转液体和价值 - 固体在Square Lattice上：Singlet和Triplet激发的见解
Gapless spin liquid and valence-bond solid in the $J_1-J_2$ Heisenberg model on the square lattice: insights from singlet and triplet excitations
论文作者
论文摘要
平方晶格上的自旋$ 1/2 $ $ J_1-J_2 $ HEISENBERG模型是最简单的示例之一，其中磁相互作用的expets可能会抑制磁性顺序，最终导致没有本地订单参数的纯量子相。在过去的三十年中，该模型已经进行了广泛的研究，结果矛盾。在这里，通过使用Gutzwiller-Projected波浪函数，并最近开发了评估低能频谱的方法，我们显示了最低能量的三胞胎和Singlet激发之间的水平交叉，以$ j_2/j_1 \约0.54美元的价格存在。这一事实支持了无间隙旋转液体之间存在相变的存在（稳定为$ 0.48 \ lisssim j_2/j_1 \ lysesim 0.54 $）和价值固体（价格为0.54美元\ lisssim j_2/j_2/j_1 \ lyssim 0.6 $），即使没有明确的符号，也没有明确的符号。这些结果证实了最近对圆柱簇的密度重新归一化计算[L.王和A.W. Sandvik，物理。莱特牧师。 121，107202（2018）]调和多年来在不同方法中获得的矛盾结果。
The spin-$1/2$ $J_1-J_2$ Heisenberg model on the square lattice represents one of the simplest examples in which the effets of magnetic interactions may suppress magnetic order, eventually leading to a pure quantum phase with no local order parameters. This model has been extensively studied in the last three decades, with conflicting results. Here, by using Gutzwiller-projected wave functions and recently developed methods to assess the low-energy spectrum, we show the existence of a level crossing between the lowest-energy triplet and singlet excitations for $J_2/J_1 \approx 0.54$. This fact supports the existence of a phase transition between a gapless spin liquid (which is stable for $0.48 \lesssim J_2/J_1 \lesssim 0.54$) and a valence-bond solid (for $0.54 \lesssim J_2/J_1 \lesssim 0.6$), even though no clear sign of dimer order is visible in the correlations functions. These results, which confirm recent density-matrix renormalization calculations on cylindrical clusters [L. Wang and A.W. Sandvik, Phys. Rev. Lett. 121, 107202 (2018)] reconcile the contraddicting results obtained within different approaches over the years.
