论文标题
可视化量子相并通过非线性维度降低识别量子相变
Visualizing Quantum Phases And Identifying Quantum Phase Transitions By Nonlinear Dimensionality Reduction
论文作者
论文摘要
识别量子阶段和相变是了解统计物理中复杂现象的关键。在这项工作中，我们提出了一种非常规的策略，以基于基于希尔伯特空间中基态的分布来访问量子阶段和相变。通过使用无监督的机器学习方法将希尔伯特空间中的量子状态映射到二维特征空间上，可以直接指定不同的阶段，并且可以很好地识别量子相变。在几个密切相关的自旋系统中，我们的建议在间隙，关键和拓扑阶段的基准测试。由于该建议直接从量子状态的分布中学习量子相和相变，因此它不需要先验了解物理系统的顺序参数，因此表明了一种感知途径，以识别量子相和相位过渡，尤其是通过学习可视化复杂系统。
Identifying quantum phases and phase transitions is key to understand complex phenomena in statistical physics. In this work, we propose an unconventional strategy to access quantum phases and phase transitions by visualization based on the distribution of ground states in Hilbert space. By mapping the quantum states in Hilbert space onto a two-dimensional feature space using an unsupervised machine learning method, distinct phases can be directly specified and quantum phase transitions can be well identified. Our proposal is benchmarked on gapped, critical, and topological phases in several strongly correlated spin systems. As this proposal directly learns quantum phases and phase transitions from the distributions of the quantum states, it does not require priori knowledge of order parameters of physical systems, which thus indicates a perceptual route to identify quantum phases and phase transitions particularly in complex systems by visualization through learning.
