Loschmidt echo singularities as dynamical signatures of strongly localized phases

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.

23 pages, 11 figures (8 main text + 3 in Appendices)

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Cited by in corpus (10)

• Ergodicity breaking in an incommensurate system observed by OTOCs and Loschmidt Echoes: From quantum diffusion to sub-diffusion
• Dynamical quantum phase transitions in Stark quantum spin chains
• The time crystal phase emerges from the qubit network under unitary random operations
• Quench dynamics of quasi-periodic systems exhibiting Rabi oscillations of two-level integrals of motion
• Sudden quench of harmonically trapped mass-imbalanced fermions
• Relaxation dynamics in the alternating XY chain following a quantum quench
• Loschmidt echo and Momentum Distribution in a Kitaev Spin Chain
• Dynamical quantum phase transitions on random networks
• Beyond the imbalance: site-resolved dynamics probing resonances in many-body localization
• Local density of states and scattering rates across the many-body localization transition