Loschmidt echo singularities as dynamical signatures of strongly localized phases
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arXiv
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| Format: | Preprint |
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2020
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| author | Benini, Leonardo Naldesi, Piero Römer, Rudolf A. Roscilde, Tommaso |
| author_facet | Benini, Leonardo Naldesi, Piero Römer, Rudolf A. Roscilde, Tommaso |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_12719 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Loschmidt echo singularities as dynamical signatures of strongly localized phases Benini, Leonardo Naldesi, Piero Römer, Rudolf A. Roscilde, Tommaso Disordered Systems and Neural Networks Quantum Gases 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. |
| title | Loschmidt echo singularities as dynamical signatures of strongly localized phases |
| topic | Disordered Systems and Neural Networks Quantum Gases |
| url | https://arxiv.org/abs/2008.12719 |