Area-Law Entanglement in Quantum Chaotic System

TL;DR

This paper presents a fully chaotic quantum many-body system that defies the typical volume-law entanglement scaling, exhibiting a strict area-law due to Hilbert space constraints, challenging the use of entanglement as a chaos indicator.

Contribution

It introduces a novel Floquet system with blockade constraints causing bounded entanglement, and establishes a duality linking constrained many-body systems to single-particle quantum walks.

Findings

Chaotic system with bounded entanglement entropy despite thermalization.

Hilbert space structure can restrict entanglement growth.

A general method to construct systems with controlled entanglement bounds.

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 $\ln2$, 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.