|large-scale numerical methods based on wave propagation
|prof. shengjun yuan （袁声军）
common computational methods in condensed matter physics typically rely on the stationary schrödinger equation, which involves diagonalizing the hamiltonian and poses challenges for large systems. this talk primarily focuses on the transformation of solved problems from the stationary schrödinger equation to the time-dependent schrödinger equation, thereby circumventing the need for diagonalization and enabling large-scale simulations and calculations of complex systems. the main topics include: (1) the linear tbpm method, based on the tight-binding approximation, allows for non-diagonalized calculations of electronic, optical, transport, plasmonic and magnetic properties, achieved through the wave propagation. this method improves the scale by 5-6 orders of magnitude compared to traditional methods, enabling the study of complex quantum systems comprising billions of atoms or even larger. typical examples of low-dimensional systems, heterostructures, fractals, and quasicrystals will be presented. (2) the linear dfpm method, based on density functional theory (dft), enables non-diagonalized self-consistent calculations of charge density and hamiltonian through wave propagation in real space. this approach extends dft to systems consisting of millions of atoms and can be applied to large-scale first-principle calculations of ground state properties (pm), molecular dynamics simulations (md), excited states (tddft), quasiparticles (gw), excitons (gw-bse), and magnetic properties (mft) based on wave propagation. (3) finally, a combined strategy of tbpm/dfpm with machine learning and an extension of the propagation method in the calculation of phonon properties and electron-phonon interactions will be discussed briefly.
shengjun yuan is a professor at the school of physics science and technology, wuhan university. he completed his undergraduate studies in the department of physics at zhejiang university in 2001. in 2003, he obtained his master's degree in theoretical physics from the university of siegen, germany, and in 2008, he earned his ph.d. in computational physics from the university of groningen, the netherlands. his main research areas are computational physics and condensed matter theory. he has developed large-scale computational methods in condensed matter physics, such as tbpm and dfpm, and independently developed multiple computational physics software, including tbplas (www.tbplas.net) based on the tight-binding model, and abplas based on density functional theory. he has published over 130 academic papers in journals such as nature, science, nature sub-journals, phys. rev. x, and phys. rev. lett., including 69 papers in the phys. rev. series.