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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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In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
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Spin–Spin Coupling: One-Bond Coupling01:17

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Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
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The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved...
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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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Tuning between Continuous Time Crystals and Many-Body Scars in Long-Range XYZ Spin Chains.

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We introduce a novel spin model exhibiting both continuous time crystals (CTCs) and quantum many-body scars (QMBS). This system allows tuning between these distinct dynamical phenomena, revealing a coexistence regime.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Dynamics
  • Statistical Mechanics

Background:

  • Persistent oscillatory dynamics in nonequilibrium systems signify ergodicity breakdown, with discrete time crystals and quantum many-body scars (QMBS) as key examples.
  • Discrete time crystals break Z_{2} symmetry under external drives, while QMBS arise from nonthermalizing eigenstates within an su(2) algebra representation.
  • The relationship and potential tunability between these phenomena remain largely unexplored.

Purpose of the Study:

  • To investigate the existence of a physical system that can exhibit both continuous time crystal (CTC) and quantum many-body scar (QMBS) behaviors.
  • To explore the possibility of tuning between these two dynamical phenomena within a single model.
  • To map the dynamical phase diagram and identify regimes of coexistence.

Main Methods:

  • Introduction of a long-range XYZ spin model in an undriven, energy-conserving system.
  • Numerical simulations utilizing exact diagonalization and the time-dependent variational principle.
  • Analysis extended to the thermodynamic limit to characterize phases and dynamics.

Main Results:

  • The proposed XYZ spin model hosts both a continuous time crystal (CTC) phase and quantum many-body scars (QMBS).
  • A dynamical phase diagram is mapped, revealing distinct regions for CTC and QMBS.
  • A novel regime where QMBS and CTC order coexist is identified.

Conclusions:

  • The study demonstrates the feasibility of a single physical system exhibiting both CTC and QMBS phenomena.
  • The coexistence regime offers a unique platform for studying the interplay between different types of oscillatory dynamics.
  • Experimental protocols are discussed for distinguishing and observing the similarities and differences between CTC and QMBS.