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¹H NMR: Long-Range Coupling01:27

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The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
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Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds' structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other...
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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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Spread of correlations in long-range interacting quantum systems.

P Hauke1, L Tagliacozzo

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We studied quantum information spreading in long-range interacting systems. Three distinct dynamical regimes were identified, with one regime exhibiting instantaneous correlation transmission, violating locality.

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Area of Science:

  • Quantum many-body physics
  • Condensed matter theory
  • Quantum information science

Background:

  • Understanding quantum many-body systems' nonequilibrium response is crucial for transport properties and quantum information spreading.
  • Little is known about the dynamics of systems with long-range interactions.

Purpose of the Study:

  • To analyze the nonequilibrium dynamics of a quantum many-body system with long-range interactions.
  • To investigate how quantum information spreads in such systems under a local quantum quench.

Main Methods:

  • Analysis of a local quantum quench in the long-range Ising model in a transverse field.
  • Utilizing complementary numerical and analytical techniques.
  • Numerical calculation of the entanglement spectrum.

Main Results:

  • Identified three dynamical regimes based on the decay exponent (α) of interactions: short-range-like (α>2), weakly long range (1<α<2), and fully nonlocal (α<1).
  • The fully nonlocal regime exhibits instantaneous correlation transmission, breaking generalized Lieb-Robinson bounds and locality.
  • Entanglement spectrum analysis confirms the validity of propagating quasiparticles, providing an intuitive interpretation of the observed dynamics.

Conclusions:

  • The dynamical behavior of quantum many-body systems with long-range interactions is highly sensitive to the interaction decay exponent.
  • The breakdown of locality in the fully nonlocal regime has significant implications for quantum information processing and theoretical models.
  • Findings can be experimentally verified in state-of-the-art trapped-ion experiments.