Sample generation for the spin-fermion model using neural networks
Sample generation for the spin-fermion model using neural networks
复制标题
使用神经网络生成自旋费米子模型的样本
DOI：
10.1103/physrevb.106.205112
复制
发表时间：
2022
影响因子：
3.7
通讯作者：
Feiguin, Adrian E.
中科院分区：
文献类型：
--
作者：
Stratis, Georgios;Weinberg, Phillip;Imbiriba, Tales;Closas, Pau;Feiguin, Adrian E.
混合量子经典模型（例如双交换哈密顿量）的蒙特卡罗模拟需要计算每一步量子自由度的状态密度。不幸的是，精确对角化的计算复杂性随着系统尺寸的函数而增长，这使得它对于任何现实系统来说都过于昂贵。我们考虑利用数据驱动的方法，即神经网络，来取代精确的对角化步骤，以加快样本生成速度。我们探索了一种学习每种自旋构型的自由能的模型，以及学习哈密顿量特征值的第二个模型。我们利用哈密顿量的对称性来人为地扩大我们的训练集，并通过评估几个热力学量来对不同的模型进行基准测试，从而实现数据增强。虽然这里考虑的所有模型在一维情况下都表现得非常好，但只有输出特征值的神经网络才能捕获二维中的正确行为。我们使用的架构的简单性与神经网络的模型无关形式相结合，可以实现快速样本生成，而无需研究人员的干预。
Monte Carlo simulations of hybrid quantum-classical models such as the double exchange Hamiltonian require calculating the density of states of the quantum degrees of freedom at every step. Unfortunately, the computational complexity of exact diagonalization grows as a function of the system's size, making it prohibitively expensive for any realistic system. We consider leveraging data-driven methods, namely, neural networks, to replace the exact diagonalization step in order to speed up sample generation. We explore a model that learns the free energy for each spin configuration and a second one that learns the Hamiltonian's eigenvalues. We implement data augmentation by taking advantage of the Hamiltonian's symmetries to artificially enlarge our training set and benchmark the different models by evaluating several thermodynamic quantities. While all models considered here perform exceedingly well in the one-dimensional case, only the neural network that outputs the eigenvalues is able to capture the right behavior in two dimensions. The simplicity of the architecture we use in conjunction with the model agnostic form of the neural networks can enable fast sample generation without the need of a researcher's intervention.
影响因子：
56.9
作者：
Carleo, Giuseppe;Troyer, Matthias
通讯作者：
Troyer, Matthias