Data for Loschmidt echo singularities as dynamical signatures of strongly localized phases

In the case of fermionic systems and S=1/2 spin models, such conserved quantities take the form of effective two-level systems, called l-bits. While their existence is the defining feature of localized phases, their direct experimental observation remains elusive.

Here we show that strongly localized l-bits bear a dramatic universal signature, accessible to state-of-the-art quantum simulators, in the form of periodic cusp singularities in the Loschmidt echo following a quantum quench from a Neel/charge-density-wave state. Such singularities are perfectly captured by a simple model of Rabi oscillations of an ensemble of independent two-level systems, which also reproduces the short-time behavior of the entanglement entropy and the imbalance dynamics.