Loschmidt echo singularities as dynamical signatures of strongly localized phases

Quantum localization (single-body or many-body) comes with the emergence of local conserved quantities-whose conservation is precisely at the heart of the absence of transport through the system. 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. In the case of interacting localized phases, the dynamics at longer times shows a sharp crossover to a faster decay of the Loschmidt echo singularities, offering an experimentally accessible signature of the interactions between l-bits.

Automated summary

The study shows that strongly localized l-bits exhibit a dramatic universal feature in the form of periodic cusp singularities in the Loschmidt echo. These singularities can be perfectly captured by a simple model of Rabi oscillations and offer an experimentally accessible signature of interactions between l-bits in interacting localized phases.