Vieijra Tom, Casert Corneel, Nys Jannes, De Neve Wesley, Haegeman Jutho, Ryckebusch Jan, Verstraete Frank
Department of Physics and Astronomy, Ghent University, B-9000 Ghent, Belgium.
Center for Biotech Data Science, Ghent University Global Campus, 21985 Incheon, Republic of Korea.
Phys Rev Lett. 2020 Mar 6;124(9):097201. doi: 10.1103/PhysRevLett.124.097201.
Although artificial neural networks have recently been proven to provide a promising new framework for constructing quantum many-body wave functions, the parametrization of a quantum wave function with non-abelian symmetries in terms of a Boltzmann machine inherently leads to biased results due to the basis dependence. We demonstrate that this problem can be overcome by sampling in the basis of irreducible representations instead of spins, for which the corresponding ansatz respects the non-abelian symmetries of the system. We apply our methodology to find the ground states of the one-dimensional antiferromagnetic Heisenberg (AFH) model with spin-1/2 and spin-1 degrees of freedom, and obtain a substantially higher accuracy than when using the s_{z} basis as an input to the neural network. The proposed ansatz can target excited states, which is illustrated by calculating the energy gap of the AFH model. We also generalize the framework to the case of anyonic spin chains.
尽管最近已证明人工神经网络为构建量子多体波函数提供了一个有前景的新框架，但由于基的依赖性，用玻尔兹曼机对具有非阿贝尔对称性的量子波函数进行参数化会固有地导致有偏差的结果。我们证明，通过在不可约表示的基而不是自旋的基中进行采样可以克服这个问题，对于不可约表示的基，相应的假设尊重系统的非阿贝尔对称性。我们应用我们的方法来寻找具有自旋1/2和自旋1自由度的一维反铁磁海森堡（AFH）模型的基态，并且获得了比使用(s_{z})基作为神经网络的输入时显著更高的精度。所提出的假设可以针对激发态，这通过计算AFH模型的能隙得到了说明。我们还将该框架推广到任意子自旋链的情况。
