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Journal Articles New Journal of Physics Year : 2021

Loschmidt echo singularities as dynamical signatures of strongly localized phases

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Leonardo Benini
Piero Naldesi
Tommaso Roscilde

Abstract

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.
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Dates and versions

hal-03636463 , version 1 (10-04-2022)

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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⟩
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