论文标题
基于有效的神经网络基于变异性蒙特卡洛方案，用于在沮丧的量子系统中直接优化激发能状态
Efficient neural-network based variational Monte Carlo scheme for direct optimization of excited energy states in frustrated quantum systems
论文作者
论文摘要
我们研究了价值键基相关物乘积ansatz的适用性，相当于受限制的Boltzmann机器量子人工神经网络ANSATZ，以及变异的蒙特卡洛方法直接优化激发能量状态，以研究强烈相关和沮丧的量子系统的性能。通过最小化能量本征态的变异功能，可以直接优化特定的能量状态，而无需了解较低的能量状态，从而可以找到能量本质。这种方法与众多张量网络或人工神经网络ANSATZ波函数相结合，然后通过考虑这些系统的属性以外的基态性能以外的这些系统，可以进一步深入了解量子相和相变。同样，该方法通常适用于任何维度，并且没有符号不稳定。我们考虑的一个例子是方格J1-J2抗铁磁磁性海森贝格模型。该模型是沮丧的量子磁性中研究最多的模型之一，因为它与高-TC超导材料中的抗磁磁序的消失密切相关，并且在J2/J1 = 0.5附近的高度挫败感方案中该系统的性质仍然没有一致。对于J1-J2模型，我们以两个位点相关因子和价键基的基础来编写变异性ANSATZ，并计算出高度沮丧的j2/j1 = 0.5的最低能量特征状态，其中该系统具有顺磁相。我们发现我们的结果与先前获得的结果非常吻合，这些结果证实了该方法研究挫败旋转系统的适用性。
We examine applicability of the valence bond basis correlator product state ansatz, equivalent to the restricted Boltzmann machine quantum artificial neural network ansatz, and variational Monte Carlo method for direct optimization of excited energy states to study properties of strongly correlated and frustrated quantum systems. The energy eigenstates are found by stochastic minimization of the variational function for the energy eigenstates which allows direct optimization of particular energy state without knowledge of the lower energy states. This approach combined with numerous tensor network or artificial neural network ansatz wavefunctions then allows further insight into quantum phases and phase transitions in various strongly correlated models by considering properties of these systems beyond the ground state properties. Also, the method is in general applicable to any dimension and has no sign instability. An example that we consider is the square lattice J1-J2 antiferromagnetic Heisenberg model. The model is one of the most studied models in frustrated quantum magnetism since it is closely related to the disappearance of the antiferromagnetic order in the high-Tc superconducting materials and there is still no agreement about the properties of the system in the highly frustrated regime near J2/J1 = 0.5. For J1-J2 model we write the variational ansatz in terms of the two site correlators and in the valence bond basis and calculate lowest energy eigenstates in the highly frustrated regime near J2/J1 = 0.5 where the system has a paramagnetic phase. We find that our results are in good agreement with previously obtained results which confirms applicability of the method to study frustrated spin systems.
