用变分Monte Carlo方法研究非阿贝尔对称和格点对称严格守恒的多体量子态
Many-Body Quantum States with Exact Conservation of Non-Abelian and Lattice Symmetries through Variational Monte Carlo
摘要：
最近，由于波函数的发展，利用变分原理优化量子态的研究出现了一个高潮。为了提高ansätze的准确性，施加系统的对称性是一种由来已久的策略。我们提出了一个全局非阿贝尔对称性固有地嵌入在其结构中的一个anomaly。我们扩展的模型，以及将晶格对称性。我们考虑了正方形晶格上的二维受抑$J_1$ - $J_2$模型的典型例子，对于该模型，本征态很难变分建模。我们的新方法保证了所得到的基态的总自旋为零。2D $J_1$ - $J_2$模型的基准测试证明了其在表示基态方面的最新性能。此外，我们的方法允许找到与所考虑的对称性（包括非阿贝尔对称性）相关联的具有确定的量子数的激发态的波函数，而不修改网络的架构。
英文摘要：
Optimization of quantum states using the variational principle has recently seen an upsurge due to developments of increasingly expressive wave functions. In order to improve on the accuracy of the ansätze, it is a time-honored strategy to impose the systems' symmetries. We present an ansatz where global non-abelian symmetries are inherently embedded in its structure. We extend the model to incorporate lattice symmetries as well. We consider the prototypical example of the frustrated two-dimensional $J_1$-$J_2$ model on a square lattice, for which eigenstates have been hard to model variationally. Our novel approach guarantees that the obtained ground state will have total spin zero. Benchmarks on the 2D $J_1$-$J_2$ model demonstrate its state-of-the-art performance in representing the ground state. Furthermore, our methodology permits to find the wave functions of excited states with definite quantum numbers associated to the considered symmetries (including the non-abelian ones), without modifying the architecture of the network.
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