Quantum Many-Body Scars

Most eigenstates of a non-integrable many-body system thermalize (ETH). But a few special "scar" states form a tower at equally-spaced energies, with anomalously low entanglement. Prepare the system in a scar state and it revives periodically — a quantum echo in a thermal bath.

Parameters

System size N: 14 Scar tower spacing ω: 1.0 Thermal spread σ: 0.5 Scar fraction: 5%

H|ψₙ⟩ = nω|ψₙ⟩ (tower)
ETH: ⟨ψₙ|O|ψₙ⟩ ≈ O(E) (thermal)

Scars were discovered in the PXP model (Bernien 2017 Rydberg experiment). They violate ETH locally, enabling quantum revivals. Blue = scar states (low entropy); orange = thermal states (high entropy, ~Page value S ≈ N/2 ln 2).