Superconductivity Model With 100,000 Equations Now Contains Just 4 Thanks to AI


A visualization of the mathematical model used to capture the physics and behavior of electrons moving on a lattice. (Domenico Di Sante/Flatiron Institute)

Electrons running through a grid-like lattice don't behave at all like pretty silver spheres in a pinball machine. They blur and bend in collective dances, following idea of a wave-like reality that are hard enough to imagine, let alone calculate. 

And yet physicist have succeeded in doing just that, measuring the motion of electrons moving about a square lattice in simulations that – until now – had needed hundreds of thousands of individual equations to produce. 

Using artificial intelligence (AI) to lessen that task down to just four equations, physicists have made their job of researching the emergent properties of complex quantum materials, a whole lot more manageable. 

In doing so, this computing feat could help deal with one of the most intractable problems of quantum physics, the 'many-electron' problem, which attempts to describe systems containing massive numbers of interacting electrons. 

It could also advance a truly useful tool for predicting electron behavior in solid state materials, the Hubbard model – all the while bettering our knowledge of how handy phases of matter, such as superconductivity, occur. 

Superconductivity is an unusual phenomenon that arises when a current of electrons flow freely through a material, losing next to no energy as they slip from one point to another. Unfortunately, most practical means of forming such a state rely on insanely low temperatures, if not extreme high pressures. Harnessing superconductivity closer to room temperature could lead to far more systematized electricity grids and devices. 

The Hubbard model is a decades-old mathematical model that explains the confusing motion of electrons through a lattice of atoms somewhat perfectly. Over the years and much to physicists' excitement, the deceptively simple model has been experimentally noticed in the behavior of a wide array of complex materials. 

With ever-increasing computer power, physicists have developed numerical simulations based on Hubbard model physics that allow them to get a strong grip on the role of the topology of the underlying lattice. 

In 2019, for instance, physicists proved the Hubble Model was capable of representing superconductivity higher-than-ultra-cold temperatures, giving the green light to researchers to utilize the model for deeper insights into the field. 

This latest study could be another big leap, greatly simplifying the number of equations required. Researchers created a machine-learning algorithm to refine a mathematical apparatus called a renormalization group, which researchers use to explore changes in a material system when properties such as temperature are altered. 

The simulations thus far only detect a relatively small number of variables in the lattice network, but the researchers anticipate their method should be fairly scalable to other systems. 

If so, it could in the future be very useful to probe the suitability of conducting materials for applications that include clean energy generation, or to aid in the design of materials that may one day gives that elusive room-temperature superconductivity. 

The biggest thing, the researchers note, will be how well the approach works on more complex quantum systems such as materials in which electrons interact at long distances. 

For now, the study demonstrates the possibility of using AI to extract compact representations of dynamic electrons, "a goal of greatest importance for the success of cutting-edge quantum field theoretical ways for tackling the many-electron problem," the researchers conclude in their abstract. 

The research was originally published in Physical Review Letters. 

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