From water boiling into steam to ice cubes melting in a glass, we have all seen the phenomenon known as phase transition in our daily lives. But there is another type of phase transition that is much harder to see, but just as striking: *quantum* phase transitions.

When cooled to near absolute zero, some materials can experience these quantum phase transitions, which can make a physicist’s jaw drop. The material may change from magnetic to non-magnetic, or it may suddenly gain the super power of conducting electricity without losing energy as heat.

The math behind these transitions is difficult to manage, even for supercomputers, but a new study from the University of Chicago suggests a new way of working with these complicated calculations, which could eventually lead to technological breakthroughs. The shortcut extracts only the most important information in the equation and creates a “map” of all possible phase transitions in the simulated system.

“This is a potentially powerful way to look at quantum phase transitions that can be used with traditional or quantum computers,” said David Mazziotti, a theoretical chemist in the Department of Chemistry and the James Franck Institute at the Institute. University of Chicago and lead author. of the study.

He and other scientists believe that if we can fully understand the complex physics at play behind quantum phase transitions, we could open the doors to new technologies. Similar discoveries in the past, for example, led to the MRI machines and transistors that make modern computers and telephones possible.

**A simplified approach**

The familiar phase changes such as evaporation and condensation occur due to temperature changes. But quantum phase transitions are triggered by some interference in their environment, such as a magnetic field.

The phenomenon occurs as a result of many electrons acting in relation to each other – a type of interaction that falls within a notoriously complex subfield known as “strongly correlated” physics. Traditionally, in order to simulate these quantum phase transitions, scientists must create a model that incorporates the possibilities of each electron. But the computing power needed to run these simulations spirals out of control very quickly.

It is believed that quantum computers are better suited to this type of problem than conventional computers, but even this method has its obstacles: for example, these problems create a ton of data that must then be translated back into the language of “ordinary” computers. . for scientists to work with them.

The researchers therefore wanted to see how they could simplify the calculation without losing precision.

Instead of creating a simulation that calculates every variable in a given quantum system, they came up with a different approach: substitute a set of numbers that describes the possible interactions between each pair of electrons. This is called a “two-electron reduced density matrix”.

“By measuring the ensemble that describes the reduced two-electron density matrix, we end up creating a map of all the different phases that the quantum system can experience,” explained graduate student Sam Warren, the first author of the paper. ‘study.

This “map” itself, he said, also offers useful benefits: “It lets you see transitions that might otherwise be missed, and it creates a really powerful visualization that lets you easily and quickly grasp a high-level overview of the system. ”