Machine-learning the angle-resolved spectral function of a hole in a quantum antiferromagnet

Understanding charge motion in a background of interacting quantum spins is a basic problem in quantum many-body physics. The most extensively studied model for this problem is the so-called t-t'-t''-J model, where the determination of the parameter t' in the context of cuprate superconductors was inconclusive. Recently we reported [1] that the model Hamiltonian parameters can be accurately predicted by using a fully connected feed-forward neural network (FFNN) to learn the angle-integrated spectral functions, i.e. the density of states (DOS), of a mobile hole in the t-t'-t''-J model. Here, we present a systematic study of the angle-resolved spectral functions. With a dataset of about 3.4x10^4 spectral functions generated in the self-consistent Born approximation, we show that the patterns produced by the principal component analysis, an unsupervised machine learning method, for k = (π/2, π/2), (π, 0), (π/2, 0) and (π/5, π/5) are ear-like, similar to those for the DOS, but heart-like for k = (0, 0) where the quasiparticle spectral weight is vanishing. Nevertheless, FFNN allows for accurate prediction of 93% of the Hamiltonian parameters by using the full k = (0, 0) spectral function with root mean squared error less than 0.007, compared with 99% for k = (π/2, π/2), (π, 0) and 100% for the DOS. Our results suggest that it may be possible to predict material parameters by deep learning angle-resolve photoemission spectroscopy (ARPES), including the laser-based ARPES where the k points are most accessible near the zone center k = (0, 0). [1] J. Lee, M. R. Carbone, and W. Yin, Phys. Rev. B 107, 205132 (2023).