标题： 掺杂二维 Hubbard 模型中时间自旋刚度和短程磁序的频率依赖性 显示英文标题

标题： Frequency dependence of temporal spin stiffness and short-range magnetic order in the doped two-dimensional Hubbard model

摘要： 我们研究在非共格磁序的平均场方法下，Hubbard模型中掺杂和温度对时间和空间自旋刚度的依赖关系。 我们表明，时间自旋刚度的频率依赖性对于获得与铜氧化物中观察到的相当的小相关长度至关重要。 利用得到的自旋刚度，在各自非线性$\sigma$模型的大-$N$极限下，我们得到了相关长度的温度和掺杂依赖性。 与La$_{2-x}$Sr$_x$CuO$_4$的实验数据一致，我们在$0.1 \lesssim x \lesssim 0.2$处获得了具有相对较短相关长度的短程磁序，并在狭窄的掺杂区域$0.05\lesssim x \lesssim 0.1$得到了磁有序基态。 后者状态可能对应于在La$_{2-x}$Sr$_x$CuO$_4$的实验数据中观察到的自旋冻结状态。 显示英文摘要

摘要： We study doping and temperature dependencies of temporal and spatial spin stiffnesses of the Hubbard model within the mean field approach for incommensurate magnetic order. We show that the frequency dependence of temporal spin stiffness is crucial to obtain small values of correlation length, comparable to those observed in cuprates. Using the obtained spin stiffnesses, we obtain the temperature and doping dependence of correlation length within the large-$N$ limit of the respective nonlinear sigma model. In agreement with the experimental data on La$_{2-x}$Sr$_x$CuO$_4$ we obtain short range magnetic order with relatively small correlation length at $0.1 \lesssim x\lesssim 0.2$, and magnetically ordered ground state in the narrow doping region $0.05\lesssim x \lesssim 0.1$. The latter state may correspond to the spin-frosen state, observed in the experimental data on La$_{2-x}$Sr$_x$CuO$_4$.