Learning Quantum Phases by Visualization
Yuan Yang, Zheng-Zhi Sun, Shi-Ju Ran, Gang Su · arXiv (Cornell University) · 2020
Identifying quantum phases of interacting many-body systems is key to understand the emergent phenomena in condensed matter physics. However, such tasks are often extremely challenging due to the exponentially large dimensionality of the associated Hilbert space. Conventional practices usually require the order parameters to specify the quantum states. In this work, we propose a different strategy to access quantum phases 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 nonlinear dimensionality reduction method, the quantum states can be explicitly visualized, from which distinct phases can be easily specified and the phase transition point can be well identified. Our scheme is benchmarked on the phases of several strongly correlated spin systems, including gapped, critical, and topological phases. As our strategy directly learns the quantum phases and phase transitions from the distributions of the quantum states, it does not depend on priori knowledge of order parameters or any other specific physical properties of the quantum systems. This work indicates a highly perceptual route to identify quantum phases and phase transitions particularly in the complex systems of condensed matter by visualization through learning.