Loschmidt echo singularities as dynamical signatures of strongly localized phases

Leonardo Benini (1) , Piero Naldesi , Rudolf Römer (1, 2) , Tommaso Roscilde

1 University of Warwick [Coventry]
2 LPTM - UMR 8089 - Laboratoire de Physique Théorique et Modélisation

Abstract 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.

Mots clés: Localization; Disordered systems; Non-equilibrium dynamics; Entanglement

Domaines: Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]

Leonardo Benini, Piero Naldesi, Rudolf Römer, Tommaso Roscilde. Loschmidt echo singularities as dynamical signatures of strongly localized phases. New Journal of Physics, 2021, 23 (2), pp.023030. ⟨10.1088/1367-2630/abdf9d⟩. ⟨hal-03636463⟩