Researchers discover efficient and highly accurate method to describe interacting electron systems

Researchers in the field of condensed matter physics face a major challenge: finding a way to accurately describe interacting electron systems in crystalline materials while keeping computational efficiency in mind. However, a new study has found a highly accurate and efficient method to tackle this problem. Led by graduate student Zheting Jin and his thesis supervisor Sohrab Ismail-Beigi from Yale Applied Physics, the research was published in Physical Review B.

Describing interacting quantum electrons accurately is difficult due to their wavy movements and interactions with each other. While dealing with these components separately is manageable, combining them creates a complex problem with no efficient solution available. Although brute force numerical solutions are theoretically possible, they require an exponential amount of computation and storage that quickly becomes infeasible for systems with more than 50 electrons. To put this into context, a single iodine atom has 53 electrons, while even a small nanoparticle can have over 1,000 electrons.

Condensed matter physics faces a significant challenge in finding computationally efficient and accurate methods to describe interacting electron systems in crystalline materials. However, a recent study published in Physical Review B has revealed a highly accurate yet efficient approach to address this problem. Led by graduate student Zheting Jin and his thesis supervisor, Sohrab Ismail-Beigi, the team has developed a method to describe interacting quantum electrons accurately, which can provide valuable insights into material behavior. However, electrons’ quantum mechanical movement and interactions with each other make their accurate description a complicated task.

The Hubbard model for interacting electrons captures the two essential components of electrons’ behavior: their desire to move around and their repulsion from other electrons. Although the model is complex, it does not offer an exact solution, and efficient and accurate methods are difficult to come by. The Ismail-Beigi team’s method is related to an approach that uses an auxiliary or subsidiary boson, requiring fewer computational resources but treating one atom at a time, leading to moderate accuracy. In contrast, the team’s approach treats two or three bonded atoms at a time, called a cluster, allowing electrons to hop between them. The clusters are then connected in a novel way to describe the entire system, offering a highly accurate description with even a relatively small cluster of three atoms. The method’s accuracy surprised the researchers, who did not expect it to perform so well.

Previous cluster approaches have failed due to prohibitive computational costs and limited accuracy. However, the Ismail-Beigi team’s approach is three to four orders of magnitude faster than benchmark calculations in the literature. The method’s efficiency allows it to run on a laptop, while benchmark calculations require a computer cluster and several days to complete. The team plans to apply this method to complex and realistic material problems shortly.

Source: Yale University

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