论文标题
用人工神经网络解决liouvillian差距
Solving the Liouvillian Gap with Artificial Neural Networks
论文作者
论文摘要
我们提出了一种获得机器学习启发的变分方法来获得Liouvillian间隙，该方法在表征开放量子系统的松弛时间和耗散相变中起着至关重要的作用。通过使用“自旋双碱基映射”，我们将密度矩阵映射到纯限制的Boltzmann-Machine（RBM）状态，然后将Liouvillian超级启动器转换为列为两位非官员操作员。 Liouvillian差距可以通过该非热门操作员的变异实时进化算法获得。我们将我们的方法应用于一个和二维的耗散海森堡模型。对于各向同性的情况，我们发现可以通过分析获得liouvillian间隙，并且在一个维度上，即使是整个Liouvillian频谱也可以使用Bethe Ansatz方法来精确解决。通过将我们的数值结果与它们的分析结果进行比较，我们表明，RBM方法可以有效地访问Liouvillian差距，无论多维性和纠缠属性如何。
We propose a machine-learning inspired variational method to obtain the Liouvillian gap, which plays a crucial role in characterizing the relaxation time and dissipative phase transitions of open quantum systems. By using the "spin bi-base mapping", we map the density matrix to a pure restricted-Boltzmann-machine (RBM) state and transform the Liouvillian superoperator to a rank-two non-Hermitian operator. The Liouvillian gap can be obtained by a variational real-time evolution algorithm under this non-Hermitian operator. We apply our method to the dissipative Heisenberg model in both one and two dimensions. For the isotropic case, we find that the Liouvillian gap can be analytically obtained and in one dimension even the whole Liouvillian spectrum can be exactly solved using the Bethe ansatz method. By comparing our numerical results with their analytical counterparts, we show that the Liouvillian gap could be accessed by the RBM approach efficiently to a desirable accuracy, regardless of the dimensionality and entanglement properties.
