Statistics of correlation functions in the random Heisenberg chain

Understand

Ergodic quantum many-body systems satisfy the eigenstate thermalization hypothesis (ETH).

• However, strong disorder can destroy ergodicity through many-body localization (MBL) -- at least in one dimensional systems -- leading to a clear signal of the MBL transition in the probability distributions of energy eigenstate expectation values of local operators.
• For a paradigmatic model of MBL, namely the random-field Heisenberg spin chain, we consider the full probability distribution of eigenstate correlation functions across the entire phase diagram.
• We find gaussian distributions at weak disorder, as predicted by pure ETH.