标题： 广义 Shastry-Sutherland 模型中$\mathbb{Z}_{2}$ Dirac 自旋液体的证据 显示英文标题

标题： Evidence for a $\mathbb{Z}_{2}$ Dirac spin liquid in the generalized Shastry-Sutherland model

摘要： 我们对最近报道的自旋-$1/2$ Shastry-Sutherland晶格上的量子自旋液体（QSL）相的性质进行了多方法研究。 在该晶格上对费米子平均场Ansätze进行全面的投影对称群分类，得到46个U(1)和80个$\mathbb{Z}_{2}$状态。 受密度矩阵重整化群（DMRG）计算的启发，这些计算表明Shastry-Sutherland模型和正方晶格$J_{1}$-$J_{2}$ Heisenberg反铁磁体可能共享相同的QSL相，我们建立了我们的Ansätze与正方晶格Ansätze之间的映射。 这使我们能够在Shastry-Sutherland系统中识别出正方晶格QSL（Z2A$zz$13）的对应物。 采用最先进的变分蒙特卡罗计算，使用通过Lanczos步骤改进的Gutzwiller投影波函数，我们证明了无能隙（狄拉克）$\mathbb{Z}_{2}$自旋液体——仅由少数参数表征——与基于神经网络量子态和DMRG的方法之间能量和关联函数的出色一致性。 此外，实空间自旋-自旋关联被证明以与$J_{1}$-$J_{2}$平方晶格模型相同的幂律衰减，该模型也包含一个$\mathbb{Z}_{2}$迪拉克自旋液体。 最后，我们应用了最近发展的伪费米子功能重正化群的基德希什形式来计算动态自旋结构因子；这些关联表现出由于激发谱中的迪拉克锥而预期的特征，从而提供了强有力的独立证据，证明存在迪拉克QSL基态。 我们发现的$d$波配对$\mathbb{Z}_{2}$迪拉克 QSL 与最近在 Pr$_2$Ga$_2$BeO$_7$中观察到的 QSL 行为的特征一致，并为未来的实验提出了预测。 显示英文摘要

摘要： We present a multimethod investigation into the nature of the recently reported quantum spin liquid (QSL) phase in the spin-$1/2$ Heisenberg antiferromagnet on the Shastry-Sutherland lattice. A comprehensive projective symmetry group classification of fermionic mean-field Ans\"atze on this lattice yields 46 U(1) and 80 $\mathbb{Z}_{2}$ states. Motivated by density-matrix renormalization group (DMRG) calculations suggesting that the Shastry-Sutherland model and the square-lattice $J_{1}$-$J_{2}$ Heisenberg antiferromagnet putatively share the same QSL phase, we establish a mapping of our Ans\"atze to those of the square lattice. This enables us to identify the equivalent of the square-lattice QSL (Z2A$zz$13) in the Shastry-Sutherland system. Employing state-of-the-art variational Monte Carlo calculations with Gutzwiller-projected wavefunctions improved upon by Lanczos steps, we demonstrate the excellent agreement of energies and correlators between a gapless (Dirac) $\mathbb{Z}_{2}$ spin liquid -- characterized by only few parameters -- and approaches based on neural quantum states and DMRG. Furthermore, the real-space spin-spin correlations are shown to decay with the same power law as in the $J_{1}$-$J_{2}$ square lattice model, which also hosts a $\mathbb{Z}_{2}$ Dirac spin liquid. Finally, we apply the recently developed Keldysh formulation of the pseudo-fermion functional renormalization group to compute the dynamical spin structure factor; these correlations exhibit the features expected due to Dirac cones in the excitation spectrum, thus providing strong independent evidence for a Dirac QSL ground state. Our finding of a $d$-wave pairing $\mathbb{Z}_{2}$ Dirac QSL is consistent with the recently observed signatures of QSL behavior in Pr$_2$Ga$_2$BeO$_7$ and outlines predictions for future experiments.