Stabilizer States at Infinite Temperature: No-Go Theorem for Two-Body Hamiltonians

Why It Matters

The theorem delineates the limits of analytic ETH constructions, informing both theoretical models and the design of quantum simulators that aim to emulate thermal behavior.

Key Takeaways

• Stabilizer eigenstates can't satisfy k‑body thermal equilibrium for k≥4.
• Two‑body nonintegrable Hamiltonians reproduce thermal values for 2‑ and 3‑body observables.
• Proof relies on graph‑state stabilizer formalism.
• Result highlights limitation of few‑body interactions for full thermalization.
• Opens path to explore higher‑spin or finite‑temperature stabilizer states.

Pulse Analysis

Understanding how isolated quantum many‑body systems reach thermal equilibrium is a central puzzle in quantum statistical mechanics. While the eigenstate thermalization hypothesis (ETH) offers a statistical explanation, analytic examples are scarce because realistic Hamiltonians involve locality and few‑body interactions. Akihiro Hokkyo and collaborators introduce a stabilizer‑based framework that generates analytically tractable zero‑energy eigenstates at infinite temperature, using graph‑state techniques to keep calculations manageable. By focusing on stabilizer states—normally tied to area‑law entanglement—the work bridges exactly solvable models and the volume‑law entanglement of true thermal states.

The core contribution is a sharp no‑go theorem: stabilizer eigenstates of any two‑body Hamiltonian cannot satisfy microscopic thermal equilibrium for observables involving four or more particles. This limitation arises from the restricted interaction range, which blocks the stabilizer structure from encoding higher‑order correlations. The authors prove the bound is tight by constructing two explicit nonintegrable two‑body Hamiltonians whose stabilizer eigenstates reproduce thermal expectation values for all two‑ and three‑body observables, confirming partial ETH compliance up to three‑body correlations.

These results suggest that advancing analytic ETH studies will require hybrid approaches that add ‘magic’ or higher‑spin degrees of freedom beyond pure stabilizer states. Extending the analysis to finite temperatures or richer interaction graphs could enable simulation of thermal pure states on quantum hardware. Overall, the work highlights a fundamental trade‑off between interaction locality and the depth of thermalization that can be captured analytically, guiding future theoretical and experimental quantum‑simulation efforts.