论文标题
$ J_1 $ - $ J_3 $ HEISENBERG模型的相图和磁激发
Phase diagram and magnetic excitations of $J_1$-$J_3$ Heisenberg model on the square lattice
论文作者
论文摘要
我们使用密度矩阵重新归一化组，精确对角线化（ED）和簇扰动理论（CPT）研究了平方晶格上的Spin-1/2 J1-J3模型的相图和动力学自旋结构因子。通过推断顺序参数并研究低洼能量和纠缠光谱的水平交叉点，我们获得了该模型的相图，并确定了量子旋转液体（QSL）相狭窄的区域，然后在中间区域中的plaquette Valence-bond-bond固体（PVB）状态，其性质在多年来一直在争议多年。更重要的是，我们使用CPT和ED来研究QSL和PVB阶段中的动力自旋结构因子。在QSL阶段，高能量镁模式完全变成了X和M点周围的一些分散弱激发。对于PVB阶段，低能频谱的特征是散布的三重激发，在高能量下，我们找到了带有宽连续的分散激励的另一个分支，这与2x2棋盘板模型中的plaquette阶段不同。在后一种情况下，由于斑块的局部激发之间的有效相互作用弱，激发的第二个分支几乎是平坦的。在J1-J3 Heisenberg模型中，PVBS相的均匀相互作用和自发翻译对称性破坏使激发光谱的差异。
We study the phase diagram and the dynamical spin structure factor of the spin-1/2 J1-J3 Heisenberg model on the square lattice using density matrix renormalization group, exact diagonalization (ED), and cluster perturbation theory (CPT). By extrapolating the order parameters and studying the level crossings of the low-lying energy and entanglement spectra, we obtain the phase diagram of this model and identify a narrow region of quantum spin liquid (QSL) phase followed by a plaquette valence-bond solid (PVBS) state in the intermediate region, whose nature has been controversial for many years. More importantly, we use CPT and ED to study the dynamical spin structure factor in the QSL and the PVBS phase. In the QSL phase, the high-energy magnon mode completely turns into some dispersive weak excitations around the X and M points. For the PVBS phase, the low-energy spectrum is characterized by a gapped triplet excitation, and at the high energy, we find another branch of dispersive excitation with broad continua, which is unlike the plaquette phase in the 2x2 checkerboard model. In the latter case, the second branch of excitation is nearly flat due to the weak effective interactions between the local excitations of the plaquettes. And in the J1-J3 Heisenberg model, the uniform interactions and the spontaneously translational symmetry breaking of the PVBS phase make the difference in the excitation spectra.
