Area-Law Entanglement in Quantum Chaotic System
Abstract
Entanglement entropy is a fundamental diagnostic for quantum chaos, typically exhibiting volume-law scaling in highly excited eigenstates of chaotic many-body systems. In this work, we present a striking counterexample: a Floquet-driven quantum many-body system with Rydberg-like blockade that, despite being fully chaotic as indicated by its Wigner-Dyson level statistics and local thermalization, exhibits a strict area-law entanglement entropy. Specifically, the entanglement entropy of every Floquet eigenstate is bounded by 2, independent of system size. We trace this anomaly to the specific Hilbert space structure imposed by the blockades, which restricts the Schmidt rank across a bipartition. Furthermore, we generalize this discovery by establishing a duality between constrained many-body Hamiltonians and single-particle quantum walks on median graphs, and we outline a general procedure for constructing systems with an entanglement entropy bounded by a predetermined constant. Our results demonstrate that entanglement entropy alone is an insufficient diagnostic of many-body quantum chaos and highlight the profound impact of Hilbert space geometry on quantum dynamics and thermalization.
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