Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains

Understand

We investigate the eigenstate thermalization hypothesis (ETH) in integrable models, focusing on the spin-1/2 isotropic Heisenberg (XXX) chain.

• We provide numerical evidence that ETH holds for typical eigenstates (weak ETH scenario).
• Specifically, using a numerical implementation of state-of-the-art Bethe ansatz results, we study the finite-size scaling of the eigenstate-to-eigenstate fluctuations of the reduced density matrix.
• We find that fluctuations are normally distributed, and their standard deviation decays in the thermodynamic limit as L^{-1/2}, with L the size of the chain.