标题： 限制玻尔兹曼机网络与二维哈伯德模型的Jastrow相关波函数比较 显示英文标题

标题： Restricted Boltzmann machine network versus Jastrow correlated wave function for the two-dimensional Hubbard model

摘要： 我们考虑一种受限玻尔兹曼机（RBM）相关的BCS波函数作为二维Hubbard模型的基态，并研究其电子和磁性性质随空穴掺杂的变化。 我们将结果与使用传统Jastrow投影算符得到的结果进行比较。 结果表明，在变分能量方面，RBM波函数在欠掺杂区域优于Jastrow投影的波函数。 对模型中超导（SC）关联的计算显示，与Jastrow投影波函数相比，RBM波函数给出的SC关联稍弱。 RBM波函数的一个显著优势是，即使波函数中没有包含任何显式的AF序，它在欠掺杂区域也能自发地产生强烈的反铁磁（AF）关联。 相比之下，Jastrow投影波函数中的AF关联被发现非常弱。 这些和其他结果表明，RBM波函数提供了对模型相图的改进描述。 这项工作还展示了神经网络量子态（NQS）波函数在研究强关联电子系统中的强大能力。 显示英文摘要

摘要： We consider a restricted Boltzmann Machine (RBM) correlated BCS wave function as the ground state of the two-dimensional Hubbard model and study its electronic and magnetic properties as a function of hole doping. We compare the results with those obtained by using conventional Jastrow projectors. The results show that the RBM wave function outperforms the Jastrow projected ones in the underdoped region inmterms of the variational energy. Computation of superconducting (SC) correlations in the model shows that the RBM wave function gives slightly weaker SC correlations as compared to the Jastrow projected wave functions. A significant advantage of the RBM wave function is that it spontaneously gives rise to strong antiferromagnetic (AF) correlations in the underdoped region even though the wave function does not incorporate any explicit AF order. In comparison, AF correlations in the Jastrow projected wave functions are found to be very weak. These and other results obtained show that the RBM wave function provides an improved description of the phase diagram of the model. The work also demonstrates the power of neural-network quantum state (NQS) wave functions in the study of strongly correlated electron systems.