Thematic Preface:
The Phenomenon of Electron Pair Condensation: An Exploration of Exactly Solvable Models
Throughout the history of science, the study of electrons and their behavior has intrigued and challenged physicists. Understanding their collective behavior within a solid, particularly in the presence of strong correlations, has remained an active area of research.
In this article, we present a class of exactly solvable models that allow us to delve into the fascinating phenomenon of electron pair condensation. These models, applicable to any dimension d, consist of electron-hopping terms and local attractive interactions between electrons. By studying these specifically designed models, we aim to unravel the underlying nature and properties of correlated electrons.
The concept of electron pair condensation has its roots in both historical and contemporary contexts. Dating back to 1911, Heike Kamerlingh Onnes discovered superconductivity, a macroscopic quantum state in which electrons can flow without resistance. This mysterious property, observed in certain materials at very low temperatures, can be attributed to electron pairing that overcomes the usual repulsion between them.
Today, we continue to explore new materials and uncover various manifestations of electron pair condensation. For example, cuprate superconductors, discovered in the late 1980s, exhibited exceptionally high transition temperatures. Researchers worldwide have been striving to understand the origins of such unconventional superconductivity and shed light on the role of electron pairing.
In line with this ongoing pursuit for knowledge, our study focuses on elucidating the precise conditions under which electron pair condensation occurs in the exactly solvable models we propose. Through rigorous analysis and calculations, we determine that for each even number of electrons less than or equal to 1/(d+1)-filling, there exists an exact ground state wherein all electrons form pairs of a certain type.
By investigating the characteristics and properties of these electron pairs, we hope to shed light on the microscopic mechanisms underlying electron pair condensation and contribute to the overall understanding of correlated electron systems. Additionally, the exactly solvable nature of these models provides a solid foundation for further theoretical developments and investigations into more complex scenarios.
Join us on this scientific journey as we uncover the mysteries of electron pair condensation and expand our comprehension of the behavior of correlated electrons within different dimensions.
Abstract: We present a class of exactly solvable models of correlated electrons. The models are defined in any dimension $d$ and consist of electron-hopping terms and local attractive interactions between electrons. For each even number of electrons less than or equal to $1/(d+1)$-filling, we find the exact ground state in which all electrons form pairs of a certain type, and thus the models exhibit an electron-pair condensation.