It is widely accepted that the localized states in disordered systems must exhibit exponential localization with a pure point spectrum. However, we establish that this belief may be incorrect. In this work, we identify a fundamental localized quantum state in a mobility edge phase. Owing to the balancing effect of this state, the mean inverse participation ratio (MIPR) of this phase neither shows a strong dependence on system size as seen in the extended and critical phases nor undergoes further localization with increasing disorder as observed in the traditional localized phase. Instead, its MIPR is entirely independent of both system size and disorder strength, consistently manifesting as a fixed value. Further, the wave function of this state is distinctly different from those of extended, critical, and traditional localized states, exhibiting a unique fixed-length continuous spectrum nature. Our results may demonstrate the existence of a different fundamental quantum state and introduce an alternative avenue for insights into the nature of quantum states in disordered systems.

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• Anderson localization
• Cold gases in optical lattices
• Fermionic condensates