Entanglement spectrum of engineered NMR spin Hamiltonians

Experimentally characterizing the complexity of many-body quantum dynamics in physical systems is a challenging task. A new correlation metric, similar to an out-of-time-ordered correlator (OTOC), was recently used to experimentally characterize the transition between a non-interacting, Anderson localized phase, and an interacting many-body localized phase in a model NMR system [1]. Here we use eigenvalue spectrum statistics (ESS) to study the properties of this class of experimentally accessible spin Hamiltonians that can be implemented in solid-state NMR experiments. ESS has recently gained attention for the ability to differentiate between different dynamical phases in simulations. We show that this model does indeed display a rich dynamical behavior, showing Poisson, Gaussian Orthogonal Ensemble (GOE), and Gaussian Unitary Ensemble (GUE) distributions in different experimentally-accessible parameter regimes. These results can guide the design of NMR OTOC experiments to probe these dynamical transitions.

[1] K. X. Wei, C. Ramanathan, P. Cappellaro, Exploring Localization in Nuclear Spin Chains, (2016)