Chebyshev expansion of spectral functions using restricted Boltzmann machines
Chebyshev expansion of spectral functions using restricted Boltzmann machines
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DOI：
10.1103/physrevb.104.205130
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发表时间：
2021-11-24
影响因子：
3.7
通讯作者：
Feiguin, Adrian E.
中科院分区：
文献类型：
--
作者：
Hendry, Douglas;Chen, Hongwei;Feiguin, Adrian E.
计算二维系统的谱函数可以说是现代计算凝聚态物理中最紧迫的挑战之一。虽然有效的技术在较低的维度，二维系统提出了不可逾越的障碍，从量子蒙特卡罗方法中的符号问题的纠缠区域法律在张量网络为基础的方法。在此，我们提出了一种基于切比雪夫展开的谱函数和神经网络表示的波函数的变分方法。切比雪夫矩是通过递归地应用哈密顿量和投影到变分状态空间，使用修改的自然梯度下降法。我们比较这种方法与修改后的近似的谱函数，它使用的Krylov子空间构造的“切比雪夫波函数。“我们给出了正方形晶格上一维和二维海森堡模型的结果，并将它们与文献中其他方法获得的结果进行了比较。
Calculating the spectral function of two-dimensional systems is arguably one of the most pressing challenges in modern computational condensed matter physics. While efficient techniques are available in lower dimensions, two-dimensional systems present insurmountable hurdles, ranging from the sign problem in quantum Monte Carlo methods to the entanglement area law in tensor-network-based methods. We hereby present a variational approach based on a Chebyshev expansion of the spectral function and a neural network representation for the wave functions. The Chebyshev moments are obtained by recursively applying the Hamiltonian and projecting on the space of variational states using a modified natural gradient descent method. We compare this approach with a modified approximation of the spectral function which uses a Krylov subspace constructed from the "Chebyshev wave functions." We present results for the one-dimensional and two-dimensional Heisenberg model on the square lattice and compare them with those obtained by other methods in the literature.