Loschmidt echo singularities as dynamical signatures of strongly localized phases

• Published in: New journal of physics Vol. 23; no. 2; pp. 23030 - 23044
• Main Authors: Benini, Leonardo, Naldesi, Piero, Römer, Rudolf A, Roscilde, Tommaso
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01-02-2021; Institute of Physics: Open Access Journals
• Subjects: Accessibility; Charge density waves; Condensed Matter; Crossovers; Decay rate; disordered systems; Disordered Systems and Neural Networks; Entanglement; localization; non-equilibrium dynamics; Phases; Physics; Simulators; Singularities; System effectiveness; Disordered systems; Entanglement; Localization; Non-equilibrium dynamics
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/abdf9d

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 Néel/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.