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Related Concept Videos

Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

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 one, the...
Atomic Nuclei: Nuclear Magnetic Moment00:59

Atomic Nuclei: Nuclear Magnetic Moment

All atomic nuclei are positively charged. When they have a nonzero spin, they behave like rotating charges. As a consequence of their charge and spin, these nuclei generate a magnetic field (B). This, in turn, gives rise to a magnetic moment (μ), which is randomly oriented in the absence of an external magnetic field. When an external magnetic field (B0) is applied, the magnetic moment vectors can align with the field or against it in 2 + 1 orientations. A hydrogen nucleus, which is just a...
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis. This...
Atomic Nuclei: Nuclear Spin01:08

Atomic Nuclei: Nuclear Spin

All atomic particles possess an intrinsic angular momentum, or 'spin'. Electrons, protons, and neutrons each have a spin value of ½, although protons and neutrons in nuclei may have higher half-integer spins owing to energetic factors.
Atomic nuclei have a net nuclear spin, , which can have an integer or half-integer value. In atomic nuclei, the spins of protons are paired against each other but not with neutrons, and vice versa. Consequently, an even number of protons does not contribute to...
Valence Bond Theory02:42

Valence Bond Theory

Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...

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Related Experiment Video

Updated: Jun 29, 2026

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
08:55

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Published on: June 7, 2018

Chiral graviton modes in fermionic fractional Chern insulators.

Min Long1,2, Zeno Bacciconi3,4, Hongyu Lu2,5,6

  • 1Department of Physics and HK Institute of Quantum Science & Technology, The University of Hong Kong, Pokfulam Road, Hong Kong Special Administrative Region of China, People's Republic of China.

Reports on Progress in Physics. Physical Society (Great Britain)
|June 27, 2026
PubMed
Summary
This summary is machine-generated.

Chiral graviton modes, key excitations in Fractional Quantum Hall (FQH) liquids, are shown to exist in Fractional Chern Insulators (FCI) on a lattice. These modes are long-lived, offering insights for solid-state and cold atom experiments.

Keywords:
Chiral graviton modefractional Chern insulatorsfractional quantum Hall states

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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

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Setting Limits on Supersymmetry Using Simplified Models
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Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Related Experiment Videos

Last Updated: Jun 29, 2026

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
08:55

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Published on: June 7, 2018

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

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07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Area of Science:

  • Condensed Matter Physics
  • Quantum Hall Effect
  • Topological Phases of Matter

Background:

  • Chiral graviton modes are characteristic collective excitations in Fractional Quantum Hall (FQH) liquids.
  • Their existence in lattice systems, like Fractional Chern Insulators (FCI), is uncertain due to the loss of continuum symmetries.
  • Recent advancements in realizing FCIs in materials like transition metal dichalcogenides and graphene highlight the urgency of this question.

Purpose of the Study:

  • To theoretically and numerically investigate the existence and properties of chiral graviton modes in fermionic FCIs.
  • To establish a connection between FQH and FCI chiral graviton modes.
  • To provide evidence for the long-lived nature of these modes in lattice systems.

Main Methods:

  • Derivation of a lattice stress tensor operator within the fermionic Harper-Hofstadter (HH) model.
  • Establishing an adiabatic connection between FQH and FCI by interpolating between HH and Checkerboard lattice models.
  • Utilizing state-of-the-art matrix product state (MPS) and exact diagonalization (ED) simulations.
  • Performing finite-size analysis to determine the graviton mode's decay rate.

Main Results:

  • Demonstrated the existence of chiral graviton modes in fermionic FCIs.
  • Established a deep connection between lattice stress-tensor operators and correlation hole dynamics.
  • Provided strong evidence for long-lived chiral graviton modes in FCIs, even without continuous symmetries.
  • Quantified an intrinsic lattice-induced decay rate for the graviton mode, found to be small relative to its energy.

Conclusions:

  • Chiral graviton modes persist as long-lived excitations in fermionic FCIs on a lattice.
  • The findings bridge the understanding of FQH and FCI systems regarding these modes.
  • Results have significant implications for exploring FCI phases in solid-state systems and cold atom experiments, and for diagnosing topological phases.