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Related Concept Videos

Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

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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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Spin–Spin Coupling Constant: Overview01:08

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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.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...
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Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

1.3K
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.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
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NMR Spectroscopy: Spin–Spin Coupling01:08

NMR Spectroscopy: Spin–Spin Coupling

2.6K
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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Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

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1.3K
Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...
1.3K
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

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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.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
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Bell-Type Correlation at Quantum Phase Transitions in Spin-1 Chain.

Dongkeun Lee1,2, Wonmin Son1

  • 1Department of Physics, Sogang University, 35, Baekbeom-ro, Mapo-gu, Seoul 04107, Korea.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary

We identified quantum phases in spin-1 XXZ chains using a generalized Bell correlation. This method precisely detects quantum phase transitions and reveals the role of high-order terms in criticality.

Keywords:
bell-nonlocalitymany-body systemsquantum phase transition

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Quantum information

Background:

  • Quantum phase transitions (QPTs) are fundamental to understanding many-body quantum systems.
  • Identifying non-trivial quantum phases and their transitions is crucial for quantum technologies.
  • The one-dimensional spin-1 XXZ chain is a key model for studying QPTs.

Purpose of the Study:

  • To develop a novel method for identifying non-trivial quantum phases in spin-1 XXZ chains.
  • To precisely detect diverse classes of quantum phase transitions.
  • To reveal the role of high-order terms in quantum criticality.

Main Methods:

  • Generalization of bipartite Bell correlations for quantum phase identification.
  • Density-matrix renormalization group (DMRG) for obtaining ground states.
  • Matrix product state (MPS) analysis for evaluating Bell-type correlations.

Main Results:

  • A generalized Bell correlation decomposes into transverse spin correlation and high-order terms.
  • Precise identification of diverse quantum phase transitions through moments of generalized Bell correlations.
  • Elucidation of the influence and physical implications of high-order terms on criticality.

Conclusions:

  • The generalized Bell correlation serves as an effective tool for detecting quantum phases and transitions.
  • High-order terms play a significant role in the critical behavior of the spin-1 XXZ chain.
  • This approach offers new insights into the nature of quantum criticality.