Multipartite entanglement structure in the Eigenstate Thermalization Hypothesis

TL;DR

This paper investigates the multipartite entanglement structure of thermal pure states under the Eigenstate Thermalization Hypothesis (ETH) using quantum Fisher information, revealing differences from canonical states and implications for many-body dynamics.

Contribution

It provides explicit calculations of quantum Fisher information in ETH states, showing bounds and differences from canonical ensembles, and explores implications for entanglement in quenched many-body systems.

Findings

QFI bounds the canonical expression from above in ETH states

Entanglement structure differs significantly near phase transitions

QFI can be extensive even when canonical counterpart vanishes

Abstract

We study the quantum Fisher information (QFI) and, thus, the multipartite entanglement structure of thermal pure states in the context of the Eigenstate Thermalization Hypothesis (ETH). In both the canonical ensemble and the ETH, the quantum Fisher information may be explicitly calculated from the response functions. In the case of ETH, we find that the expression of the QFI bounds the corresponding canonical expression from above. This implies that although average values and fluctuations of local observables are indistinguishable from their canonical counterpart, the entanglement structure of the state is starkly different; with the difference amplified, e.g., in the proximity of a thermal phase transition. We also provide a state-of-the-art numerical example of a situation where the quantum Fisher information in a quantum many-body system is extensive while the corresponding quantity in the canonical ensemble vanishes. Our findings have direct relevance for the entanglement structure in the asymptotic states of quenched many-body dynamics.