Quench-induced entanglement and relaxation dynamics in Luttinger liquids

Abstract

We investigate the time evolution towards the asymptotic steady state of a one dimensional interacting system after a quantum quench. We show that at finite time the latter induces entanglement between right- and left- moving density excitations, encoded in their cross-correlators, which vanishes in the long-time limit. This behavior results in a universal time-decay in system spectral properties $\propto t^{-2}$, in addition to non-universal power-law contributions typical of Luttinger liquids. Importantly, we argue that the presence of quench-induced entanglement clearly emerges in transport properties, such as charge and energy currents injected in the system from a biased probe, and determines their long-time dynamics. In particular, energy fractionalization phenomenon turns out to be a promising platform to observe the universal power-law decay $\propto t^{-2}$ induced by entanglement and represents a novel way to study the corresponding relaxation mechanism.

arXiv comment11 pages, 3 figures

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• Charge and energy fractionalization mechanism in one-dimensional channels
• Unveiling operator growth in SYK quench dynamics
• Entanglement prethermalization in the Tomonaga-Luttinger model
• Disentangling Sources of Quantum Entanglement in Quench Dynamics
• Spectral properties of interacting helical channels driven by Lorentzian pulses
• Universal scaling of quench-induced correlations in a one-dimensional channel at finite temperature
• Entropy production in one-dimensional quantum fluids
• Time-dependent spectral functions of the Anderson impurity model in response to a quench with application to time-resolved photoemission spectroscopy
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• Non-thermal Tomonaga-Luttinger liquid eventually emerging from hot electrons in the quantum Hall regime
• Quench-Probe Setup as Analyzer of Fractionalized Entanglement Spreading