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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: Two-Bond Coupling (Geminal Coupling)01:20

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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.
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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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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NMR Spectroscopy: Spin–Spin Coupling01:08

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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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Atomic Nuclei: Nuclear Spin State Overview01:03

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NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of...
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Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

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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...
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Anisotropic spin-1/2 XXZ chains with uniform gamma interaction.

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This study maps the ground state phase diagram of spin-1/2 XXZ chains using iTEBD and Lanczos methods. It reveals distinct gapped and gapless phases characterized by various order parameters like magnetization and chirality.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Magnetism
  • Many-Body Systems

Background:

  • Spin-1/2 XXZ chains are fundamental models in quantum magnetism.
  • Understanding their ground state phase diagram is crucial for various physical phenomena.
  • Anisotropic interactions and uniform Gamma fields introduce complex behaviors.

Purpose of the Study:

  • To determine the intricate ground state phase diagram of anisotropic spin-1/2 XXZ chains.
  • To investigate the influence of uniform Gamma interaction on magnetic phases.
  • To characterize distinct phases using order parameters and spectral properties.

Main Methods:

  • Infinite time evolving block decimation (iTEBD) for numerical analysis.
  • Lanczos technique for obtaining ground state properties.
  • Mean-field framework with fermionic representation for analytical approximations.

Main Results:

  • Detailed mapping of the ground state phase diagram.
  • Identification of gapped and gapless domains at absolute zero.
  • Characterization of phases by magnetization, staggered magnetization, chirality, and spin nematicity.

Conclusions:

  • The study provides a comprehensive understanding of the spin-1/2 XXZ chain phase diagram.
  • Numerical and analytical methods confirm the existence of diverse phases with unique long-range order.
  • The findings contribute to the field of quantum magnetism and condensed matter theory.