We show that the rainbow state, which has volume-law entanglement entropy for most choices of bipartitions, can be embedded in a many-body localized spectrum. For a broad range of disorder strengths in the resulting model, we numerically find a narrow window of highly entangled states in the spectrum, embedded in a sea of area law entangled states. The construction hence embeds mobility edges in many-body localized systems. This can be thought of as the complement to many-body scars, an “inverted quantum many-body scar,” providing a further type of setting where the eigenstate thermalization hypothesis is violated.

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• Eigenstate thermalization
• Many-body localization
• Quantum entanglement
• Quantum scars
• Disordered systems
• Strongly correlated systems
• Spin lattice models