Eigenstate Thermalization from the Clustering Property of Correlation

Extensive Multipartite Entanglement from su(2) Quantum Many-Body Scars

Recent experimental observation of weak ergodicity breaking in Rydberg atom quantum simulators has sparked interest in quantum many-body scars-eigenstates which evade thermalization at finite energy densities due to novel mechanisms that do not rely on integrability or protection by a global symmetry. A salient feature of some quantum many-body scars is their subvolume bipartite entanglement entropy. In this Letter, we demonstrate that such exact many-body scars also possess extensive multipartite entanglement structure if they stem from an su(2) spectrum generating algebra. We show this analytically, through scaling of the quantum Fisher information, which is found to be superextensive for exact scarred eigenstates in contrast to generic thermal states. Furthermore, we numerically study signatures of multipartite entanglement in the PXP model of Rydberg atoms, showing that extensive quantum Fisher information density can be generated dynamically by performing a global quench experiment. Our results identify a rich multipartite correlation structure of scarred states with significant potential as a resource in quantum enhanced metrology.

Refining Deutsch's approach to thermalization

The groundbreaking investigation by Deutsch [Phys. Rev. A 43, 2046 (1991)PLRAAN1050-294710.1103/PhysRevA.43.2046] of how a closed many-body quantum system approaches thermal equilibrium is revisited. It is shown how to carry out some important steps that were missing in that paper. Moreover, the class of admitted systems is extended considerably.

Clustering of Conditional Mutual Information for Quantum Gibbs States above a Threshold Temperature

We prove that the quantum Gibbs states of spin systems above a certain threshold temperature are approximate quantum Markov networks, meaning that the conditional mutual information decays rapidly with distance. We demonstrate the exponential decay for short-ranged interacting systems and power-law decay for long-ranged interacting systems. Consequently, we establish the efficiency of quantum Gibbs sampling algorithms, a strong version of the area law, the quasilocality of effective Hamiltonians on subsystems, a clustering theorem for mutual information, and a polynomial-time algorithm for classical Gibbs state simulations.