Decoding flat bands from compact localized states

TL;DR

This paper presents a systematic method to generate compact localized states for flat band systems using destructive interference patterns, enabling the design of new 2D flat band models and extensions to complex systems.

Contribution

It introduces a novel, systematic approach to construct compact localized states in flat band systems through interference design, applicable to multi-orbital, quasicrystal, and disordered systems.

Findings

Developed a method to generate compact localized states in 1D chains.

Constructed new 2D flat band systems using the method.

Extended the approach to multi-orbital, quasicrystal, and disordered systems.

Abstract

The flat band system is an ideal quantum platform to investigate the kaleidoscope created by the electron-electron correlation effects. The central ingredient of realizing a flat band is to find its compact localized states. In this work, we develop a systematic way to generate the compact localized states by designing destructive interference pattern from 1-dimensional chains. A variety of 2-dimensional new flat band systems are constructed with this method. Furthermore, we show that the method can be extended to generate the compact localized states in multi-orbital systems by carefully designing the block hopping scheme, as well as in quasicrystal and disorder systems.