The research work was primarily carried out by Domenico Di Sante, an assistant professor at the University of Bologna in Italy, focused on the Hubbard model that tries to explain the transition between conducting and insulating systems.
The Hubbard Model
First proposed in 1963, the Hubbard Model tries to explain the behavior of electrons when placed on a gridlike lattice. Under the model, when two electrons occupy the same site on the lattice, they interact, and their fates become quantum mechanically entangled, even if they are placed far apart.
Studying electron behavior helps physicists explain the different phases of matter. However, since the electrons are quantum mechanically entangled, physicists must consider all the electrons together in their calculations. This makes calculations a complex mathematically hurdle that becomes exponentially harder the larger the number of electrons being considered.
To simplify the task, physicists used a mathematical apparatus called a renormalization group, which can help keep track of all electron interactions. However, a renormalization group can end up containing anywhere between tens of thousands to millions of equations that need solving.
Deploying AI to simplify
Di Sante and his colleagues wondered if AI could be used to simplify the problem at hand. They turned to neural networks, where the software first created connections between the renormalization group and then tweaked the strength of those connections to find a small set of equations that generated the same solution as the original group, Phys.org said in its report.