Neural Canonical Transformations for Quantum Anharmonic Solids of Lithium

Lithium is a typical quantum solid, characterized by cubic structures at ambient pressure. As the pressure increases, it forms more complex structures and undergoes a metal-to-semiconductor transformation, complicating theoretical and experimental analyses. We employ the neural canonical transformation approach, a variational method based on probabilistic generative models, to investigate the quantum anharmonic effects in lithium solids at finite temperatures. This approach combines a normalizing flow for phonon excited-state wave functions with a probabilistic model for the occupation of energy levels, optimized jointly to minimize the free energy. Our results indicate that quantum anharmonicity lowers the bcc-fcc transition temperature compared to classical molecular dynamics predictions. At high pressures, the predicted fractional coordinates of lithium atoms in the cI16 structure show good quantitative agreement with experimental observations. Finally, contrary to previous beliefs, we find that the poor metallic oC88 structure is stabilized by the potential energy surface obtained via high-accuracy electronic structure calculations, rather than thermal or quantum effects.