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

TL;DR

This paper develops a method to compute correlation functions in exactly-solvable flat-band models using molecular-orbital representation, revealing their gapped ground states and entanglement properties.

Contribution

It introduces a molecular-orbital framework to efficiently analyze correlation functions and entanglement in flat-band models with fully occupied bands.

Findings

Correlation functions are computed using molecular-orbitals instead of explicit wave functions.

Models exhibit gapped ground states with flat bands fully occupied.

Entanglement entropy is derived from correlation functions.

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 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.