Construction of interacting flat-band models by molecular-orbital representation: Correlation functions, energy gap, and entanglement

• Published in: Progress of theoretical and experimental physics Vol. 2022; no. 2
• Main Authors: Mizoguchi, Tomonari, Kuno, Yoshihito, Hatsugai, Yasuhiro
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.02.2022
• Subjects: Eigenvalues; I46
• ISSN: 2050-3911; 2050-3911
• DOI: 10.1093/ptep/ptac015

Abstract We calculate correlation functions of exactly solvable one-dimensional flat-band models by utilizing the “molecular-orbital” representation. The models considered in this paper have a gapped ground state with the flat band being fully occupied, even in the presence of the interaction. In this class of models, the space spanned by the molecular-orbitals is the co-space of that spanned by the flat bands. Thanks to this property, the correlation functions are calculated by using the information of the molecular-orbitals rather than the explicit forms of the flat-band wave functions, which simplifies the calculations. As a demonstration, several one-dimensional models and their correlation functions are presented. We also calculate the entanglement entropy by using the correlation function.