Construction of Flat band Quantum Scars

We propose a general construction scheme for a quantum scar state in flat band systems. The quantum scar is an atypical eigenstate breaking eigenstate thermalization hypothesis embedded in a many-body energy spectrum. In our construction, we make use of orthogonal compact localized states that are characteristics of certain flat-band models. 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. Furthermore, some examples of higher-dimensional systems are also proposed. Our construction method of quantum scar has broad applications to various flat band systems.