Related Experiment Video
Updated: Jul 27, 2026
09:00
Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
Published on: June 28, 2018
Dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
R G Pereira1, J Sirker, J-S Caux
1Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1.
Physical Review Letters
|August 16, 2006
Summary
We analyzed the XXZ-chain
Area of Science:
- Condensed Matter Physics
- Quantum Magnetism
- Statistical Mechanics
Background:
- The XXZ-chain is a fundamental model in quantum magnetism.
- Understanding its spin structure factor is crucial for characterizing magnetic properties.
Purpose of the Study:
- To investigate the longitudinal spin structure factor of the XXZ-chain at small wave vectors.
- To analyze the impact of magnetic fields on the spin structure factor's properties.
Main Methods:
- Bethe ansatz
- Field theory methods
- Density matrix renormalization group (DMRG)
Main Results:
- The spin structure factor exhibits a non-Lorentzian peak and a high-frequency tail.
- Peak width scales as q^2 in a finite magnetic field, and q^3 at zero field.
- An analytic formula for the tail was derived, showing integrability's effect on line shape.
Conclusions:
- The study provides detailed insights into the longitudinal spin structure factor of the XXZ-chain.
- Integrability plays a direct role in shaping the observed spectral features.
- The findings are relevant for understanding quantum magnetic systems.
Related Concept Videos
03:06The Pauli Exclusion Principle
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
02:42Valence 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...
01:03Atomic 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...
01:14Atomic 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.
01:08Spin–Spin Coupling Constant: Overview
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 have a...
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 have a...
01:17Spin–Spin Coupling: One-Bond Coupling
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,...