The Determination of Phases of Wave Functions

G. F. Drukarev

Louis C. Green

Tomi Ohtsuki, Tomohiro Mano

Applications of neural networks to condensed matter physics are becoming popular and beginning to be well accepted. Obtaining and representing the ground and excited state wave functions are examples of such applications. Another application is analyzing the wave functions and determining their quantum phases. Here, we review the recent progress of using the multilayer convolutional neural network, so-called deep learning, to determine the quantum phases in random electron systems. After training the neural network by the supervised learning of wave functions in restricted parameter regions in known phases, the neural networks can determine the phases of the wave functions in wide parameter regions in unknown phases; hence, the phase diagrams are obtained. We demonstrate the validity and generality of this method by drawing the phase diagrams of two- and higher dimensional Anderson metal-insulator transitions and quantum percolations as well as disordered topological systems such as three-dimensional topological insulators and Weyl semimetals. Both real-space and Fourier space wave functions are analyzed. The advantages and disadvantages over conventional methods are discussed.

Zheng-Min Wang, Daniel S. Elliott

We establish a technique for the determination of the phase difference between even and odd parity continuum wave functions in atoms. This determination is based upon our detailed measurements of a quantum mechanical interference between two photoionization processes using a two-color laser field. We present our measurement of the phase difference between the continuum p and d waves in atomic rubidium, which is in good agreement with the expected value.