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New theoretical physics research introduces a simulation method of machine-learning-based effective Hamiltonian for super-large-scale atomic structures. This effective Hamiltonian method could simulate much larger structures than the methods based on quantum mechanisms and classical mechanics.

The are published in npj Computational Materials under the title, "Active learning of effective Hamiltonian for super-large-scale atomic structures." The paper was authored by an international team of physicists, including the University of Arkansas, Nanjing University, and the University of Luxembourg.

In ferroelectrics and dielectrics, there is one kind of structure—mesoscopic structure, which usually has atoms more than millions.

The large structures are beyond the computational ability of conventional methods based on quantum mechanism and classical mechanics, while the effective Hamiltonian methods could easily handle them. It is one of the fastest atomic scale computational methods, and will be a powerful scientific tool in the study of mesoscopic structures and materials.

Effective Hamiltonian is an energy expression with kinds of coupling terms, and the parameters of the terms can be obtained by quantum mechanics methods. The conventional way of obtaining the parameters is usually complex.

A new way is proposed based on machine learning to compute the parameters in this paper. This machine-learning approach provides a universal and automatic way to compute the parameters of the effective Hamiltonian for any considered complex systems with super-large-scale atomic structures.

By using the new effective Hamiltonian methods, scientists could design new materials with desirable properties, such as ferroelectric and piezoelectric properties, by large atomic-scale structure simulation.

The next step in developing the effective Hamiltonian methods is to propose a general effective Hamiltonian based on the lattice Wannier function and symmetry. Then any structure distortion and phase transitions could be mimicked, and additional properties, such as thermal properties, could also be simulated.