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Related Concept Videos

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.
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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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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.
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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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Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
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Two-Fluid Coexistence in a Spinless Fermions Chain with Pair Hopping.

Lorenzo Gotta1, Leonardo Mazza1, Pascal Simon2

  • 1Université Paris-Saclay, CNRS, LPTMS, 91405 Orsay, France.

Physical Review Letters
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A novel phase reveals coexistence between paired and unpaired fermions in a one-dimensional model. This finding, supported by numerical calculations, advances understanding of quantum many-body systems.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Systems
  • Low-Dimensional Materials

Background:

  • Understanding emergent phenomena in one-dimensional (1D) quantum systems is crucial.
  • Fermionic systems exhibit complex behaviors, including pairing and Luttinger liquid states.
  • Investigating models with novel interactions, like pair hopping, can uncover new phases.

Purpose of the Study:

  • To explore the phase diagram of a 1D model of spinless fermions with pair hopping.
  • To identify and characterize novel quantum phases arising from pair hopping interactions.
  • To elucidate the coexistence of different fermionic states within a single phase.

Main Methods:

  • Numerical density-matrix renormalization-group (DMRG) calculations were extensively performed.
  • A theoretical two-fluid model was developed to interpret the numerical findings.
  • Analysis focused on identifying distinct fermionic liquid behaviors.

Main Results:

  • A novel phase was discovered where a Luttinger liquid of paired fermions coexists with a Luttinger liquid of unpaired fermions.
  • The coexistence is robust and characterized by distinct electronic fluid behaviors.
  • The numerical results align with the predictions of the two-fluid model.

Conclusions:

  • The 1D spinless fermion model with pair hopping hosts a unique coexistence phase.
  • This phase provides a new platform for studying interacting quantum fluids.
  • The findings contribute to the fundamental understanding of quantum phase transitions and emergent phenomena in 1D systems.