  The critical state in disordered systems, a fascinating and subtle
eigenstate, has attracted a lot of research interest. However, the nature of
the critical state is difficult to describe quantitatively. Most of the studies
focus on numerical verification, and cannot predict the system in which the
critical state exists. In this work, we propose an explicit and universal
criterion that for the critical state Lyapunov exponent should be 0
simultaneously in dual spaces, namely Lyapunov exponent remains invariant under
Fourier transform. With this criterion, we exactly predict a specific system
hosting a large number of critical states for the first time. Then, we perform
numerical verification of the theoretical prediction, and display the
self-similarity and scale invariance of the critical state. Finally, we
conjecture that there exist some kind of connection between the invariance of
the Lyapunov exponent and conformal invariance.
