Phase Transitions in 2D Hubbard Model Revealed by Single-Site Entropy

On May 1, 2025, Willdauany C. de Freitas Silva and four co-authors published Single-site entanglement as a marker for quantum phase transitions at non-zero temperatures, demonstrating how single-site entanglement can signal phase transitions in quantum systems using Monte Carlo simulations on the two-dimensional Hubbard model.

The study investigates phase transitions in strongly correlated systems using von Neumann entropy as a measure of quantum entanglement. By applying Monte Carlo calculations to the two-dimensional Hubbard model across different geometries, researchers demonstrate that the average single-site von Neumann entropy effectively signals phase transitions at finite temperatures. Additionally, a linear relationship between this entropy and magnetic susceptibility is observed in all geometries, suggesting that susceptibility can be used to estimate entropy experimentally. These findings provide insights into quantum phase transitions and offer practical guidance for experimental measurements.

Quantum Entanglement: A New Frontier in Materials Science

In the realm of quantum physics, entanglement has long captivated scientists with its ability to connect particles across vast distances. Beyond theoretical fascination, recent research reveals that this phenomenon significantly influences material properties, particularly in phase transitions and electronic behaviors. This article explores how quantum entanglement is reshaping our understanding of condensed matter physics, offering fresh insights into materials and their applications.

Entanglement’s Influence on Material Transformations

Phase transitions, such as the shift from metal to insulator, are fundamental processes in materials science. Traditionally explained through band theory, these transitions are now understood to involve quantum entanglement as a key driver. The Hubbard model, which describes electron interactions in solids, highlights this role. Studies on the kagome lattice—a hexagonal arrangement of atoms—show that entanglement can create intermediate phases between metals and insulators, challenging conventional theories.

Beyond Band Theory: Correlations and Entanglement

The Hubbard model also illuminates how strong electron correlations affect material behavior. In the kagome lattice, these correlations can produce insulating phases where band theory predicts metallicity. This phenomenon, known as a correlated insulator, underscores entanglement’s stabilising role. Additionally, the ionic Hubbard model demonstrates that entanglement influences magnetic and transport properties, particularly in two-dimensional systems where geometric constraints amplify quantum effects.

Technological Implications and Future Research

Understanding entanglement’s impact on phase transitions could revolutionise material design, aiding in the creation of high-temperature superconductors and advanced quantum technologies. However, challenges remain, notably the fermion sign problem, a computational hurdle in studying many-particle systems. Despite this, ongoing research continues to unravel the interplay between entanglement, correlations, and material properties, promising breakthroughs in both fundamental science and technology.

Conclusion

Quantum entanglement is emerging as a cornerstone of modern condensed matter physics, challenging traditional theories and opening new avenues for understanding materials. As researchers continue to explore this phenomenon, we may unlock unprecedented technological advancements, transforming our approach to materials science.