Condensed Matter Theory

Abstract:

We discuss eigenstate correlations for ergodic, spatially extended many-body quantum systems, in terms of the statistical properties of matrix elements of local observables. While the eigenstate thermalization hypothesis (ETH) is known to give an excellent description of these quantities, the phenomenon of scrambling and the butterfly effect imply structure beyond ETH. We determine the universal form of this structure at long distances and small eigenvalue separations for Floquet systems. We use numerical studies of a Floquet quantum circuit to illustrate both the accuracy of ETH and the existence of our predicted additional correlations.

Abstract:

Comparisons and analogies are drawn between materials ferroic glasses and conventional spin glasses, in terms of both experiment and theoretical modelling, with inter-system conceptual transfers leading to suggestions of further issues to investigate.