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Related Concept Videos

Chirality02:25

Chirality

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Chirality is a term that describes the lack of mirror symmetry in an object. In other words, chiral objects cannot be superposed on their mirror images. For example, our feet are chiral, as the mirror image of the left foot, the right foot, cannot be superposed on the left foot.
Chiral objects exhibit a sense of handedness when they interact with another chiral object. For example, our left foot can only fit in the left shoe and not in the right shoe. Achiral objects — objects that have...
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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

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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: 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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Chirality in Nature02:30

Chirality in Nature

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Chirality is the most intriguing yet essential facet of nature, governing life’s biochemical processes and precision. It can be observed from a snail shell pattern in a macroscopic world to an amino acid, the minutest building block of life. Most of the snails around the world have right-coiled shells because of the intrinsic chirality in their genes. All the amino acids present in the human body exist in an enantiomerically pure state, except for glycine - the sole achiral amino acid.
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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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Chiral Gapless Spin Liquid in Hyperbolic Space.

Felix Dusel1, Tobias Hofmann1, Atanu Maity1

  • 1Julius-Maximilians-Universität, Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, 97074 Würzburg, Germany.

Physical Review Letters
|July 31, 2025
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Summary
This summary is machine-generated.

Researchers studied the Kitaev model on a {9,3} hyperbolic lattice, discovering a gapless chiral Z_{2} spin liquid. This state exhibits spontaneous time-reversal symmetry breaking and may host exotic quasiparticles.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Materials
  • Topological Phases of Matter

Background:

  • The Kitaev model describes quantum spin liquids, exotic states of matter.
  • Hyperbolic lattices offer new geometries for realizing novel quantum phenomena.
  • Generalizing the Kitaev model to non-Euclidean spaces is crucial for exploring new physics.

Purpose of the Study:

  • To investigate the Kitaev model on the {9,3} hyperbolic lattice.
  • To identify the ground state properties and emergent phenomena in this system.
  • To explore the potential for novel topological phases and quasiparticles.

Main Methods:

  • Analysis of the bulk spectrum for large finite size droplets.
  • Utilizing a three-color bond coding for Kitaev Ising spin couplings.
  • Generalizing the Kitaev model to a hyperbolic tiling of nonagons.

Main Results:

  • Identification of a gapless chiral Z_{2} spin liquid state.
  • Observation of spontaneous time-reversal symmetry breaking.
  • The hyperbolic spin liquid is conjectured to feature chiral quasiparticles.

Conclusions:

  • The {9,3} hyperbolic lattice hosts a unique chiral spin liquid state.
  • The noncommutative translation group structure suggests non-Abelian properties for quasiparticles.
  • This work opens avenues for exploring topological quantum matter on hyperbolic geometries.