Finite-size scaling of eigenstate thermalization

Understand

According to the eigenstate thermalization hypothesis (ETH), even isolated quantum systems can thermalize because the eigenstate-to-eigenstate fluctuations of typical observables vanish in the limit of large systems.

• Of course, isolated systems are by nature finite, and the main way of computing such quantities is through numerical evaluation for finite-size systems.
• Therefore, the finite-size scaling of the fluctuations of eigenstate expectation values is a central aspect of the ETH.
• In this work, we present numerical evidence that for generic non-integrable systems these fluctuations scale with a universal power law $D^{-1/2}$ with the dimension $D$ of the Hilbert space.