Electrons traveling through a mesh-like lattice do not behave like the pretty silver balls of a pinball machine. They blur and bend in group dances, following the whims of a wave-like reality that is hard to imagine, let alone compute.

However, the scientists succeeded in doing just that, capturing the motion of electrons moving around a square-shaped lattice in simulations that would – until now – require hundreds of thousands of individual equations to produce.

Use Artificial intelligence (AI) To reduce this task to just four equations, physicists have made their task of studying the emerging properties of complex quantum materials much easier.

By doing so, this computational work could help address one of the most intractable problems of quantum physics, the “many electrons” problem, which attempts to describe systems with large numbers of interacting electrons.

Can also submit a file A truly legendary tool To predict electron behavior in solids, Hubbard model – all while improving our understanding of how easy matter phases are, such as superconductivityto speak.

Superconductivity is a strange phenomenon that arises when a stream of electrons flows unimpeded through a material, losing any energy as it slides from one point to another. Unfortunately, the most practical means of creating such a state relies on insanely low temperatures, if not Ridiculously high pressure. Harnessing superconductivity near room temperature could lead to more efficient electrical networks and devices.

Since achieving superconductivity under more reasonable conditions remains a lofty goal, physicists have resorted to using models to predict how electrons will behave under different conditions, and thus which materials make suitable conductors or insulators.

These models have their work cut out for them. Electrons don’t roll through the network of atoms like little balls, after all, with clearly defined positions and paths. Their activity is a potential chaos, influenced not only by their surroundings but by the history of their interaction with other electrons they bumped into on the way.

When electrons interact, their fates can be closely entangled, orentangledSimulating the behavior of a single electron means tracing the range of possibilities for all electrons in a model system simultaneously, which makes the computational challenge even more challenging.

Hubbard’s model is a decades-old mathematical model that describes the confusing motion of electrons through a network of atoms fairly accurately. Over the years and much to the delight of physicists, the deceptively simple The model has been experimentally realized in the behavior of A A wide range of complex materials.

With the ever-increasing power of computers, researchers have developed numerical simulations based on the physics of the Hubbard model that allow them to learn about the role of the underlying network topology.

In 2019, for example, researchers demonstrated that the Hubble model is able to represent superconductivity Temperatures above extreme coldgiving the green light for researchers to use the model to gain deeper insights into the field.

This new study could be another big leap, drastically simplifying the number of equations required. The researchers developed a machine-learning algorithm to improve a mathematical device called a renormalization array, which physicists use to explore changes in a material system when properties such as temperature change.

“It’s basically a machine that has the ability to detect subtle patterns,” physicist and lead author Domenico de Santi, of the University of Bologna in Italy, said. Says From the software developed by the team.

“We start with this massive object of all these paired differential equations together”—each representing pairs of entangled electrons—“and then we use machine learning To turn it into something so small you can count on your fingers, ‘De Sante Says of their approach.

The researchers show that the data-driven algorithm can efficiently learn and recapitulate the dynamics of Hubbard’s model, using as few equations — four to be exact — and without sacrificing accuracy.

“When we saw the result, we said, ‘Wow, that’s more than we expected.’ We were really able to pick up on the relevant physics,” Says De Santi.

It took weeks to train the machine-learning program with the data, but de Santi and colleagues say it can now be adapted to work on other puzzling problems with condensed matter.

The simulations so far only capture a relatively small number of variables in the mesh network, but the researchers expect their method to be somewhat scalable for other systems.

If so, it could be used in the future to verify the suitability of conductive materials for applications that include clean energy generation, or to help design materials that might one day provide the elusive room-temperature superconductivity.

The researchers note that the real test will be how well this approach works in more complex quantum systems such as materials in which electrons interact over long distances.

Currently, the work demonstrates the potential for using AI to extract compressed representations of dynamical electrons, “a goal of paramount importance to the success of sophisticated quantum field theoretical approaches to address the multiple-electron problem,” according to the researchers. deduce in the abstract.

The search was published in *physical review messages.*