Flat Band Quantum Scar

TL;DR

This paper demonstrates the construction of quantum scar states in flat band systems using orthogonal compact localized states, with numerical evidence in a saw-tooth lattice and potential applications to higher dimensions.

Contribution

It introduces a novel method to construct quantum scar states in flat band systems leveraging orthogonal compact localized states, expanding understanding of non-thermal eigenstates.

Findings

Quantum scar states can be constructed in flat band systems.

Numerical demonstration in a saw-tooth lattice confirms the presence of scar states.

The method applies broadly to various flat band systems and higher-dimensional models.

Abstract

We show that a quantum scar state, an atypical eigenstate breaking eigenstate thermalization hypothesis embedded in a many-body energy spectrum, can be constructed in flat band systems. The key idea of our construction is to make use of orthogonal compact localized states. We concretely discuss our construction scheme, taking a saw-tooth flat lattice system as an example, and numerically demonstrate the presence of a quantum scar state. Examples of higher-dimensional systems are also addressed. Our construction method of quantum scar has broad applications to various flat band systems.