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Related Concept Videos

Quantum Numbers02:43

Quantum Numbers

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It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
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The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Range00:59

Range

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The range is one of the measures of variation. It can be defined as the difference between a dataset's highest and lowest values. For example, in the study of seven 16-ounce soda cans, the filled volume of soda was measured, thus producing the following amount (in ounces) of soda:
15.9; 16.1; 15.2; 14.8; 15.8; 15.9; 16.0; 15.5
Measurements of the amount of soda in a 16-ounce can vary since different subjects record these measurements or since the exact amount - 16 ounces of liquid, was not...
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NMR Spectroscopy: Spin–Spin Coupling01:08

NMR Spectroscopy: Spin–Spin Coupling

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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...
3.2K
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

1.5K
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,...
1.5K
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

1.5K
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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Associated Chromosome Trap for Identifying Long-range DNA Interactions
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Quasiparticles in Quantum Spin Chains with Long-Range Interactions.

Laurens Vanderstraeten1, Maarten Van Damme1, Hans Peter Büchler2

  • 1Department of Physics and Astronomy, University of Ghent, Krijgslaan 281, 9000 Gent, Belgium.

Physical Review Letters
|September 20, 2018
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Summary
This summary is machine-generated.

We accurately captured quasiparticle excitations in quantum spin chains with long-range interactions. This method works even for large correlation lengths and topological excitations like spinons.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Many-body systems

Background:

  • Quantum spin chains are fundamental models in condensed matter physics.
  • Long-range interactions introduce complex behaviors not seen in short-range systems.
  • Understanding quasiparticle excitations is key to characterizing phases of matter.

Purpose of the Study:

  • To investigate quasiparticle excitations in quantum spin chains with long-range interactions.
  • To assess the accuracy of the local quasiparticle ansatz in these systems.
  • To explore the relationship between interactions, excitation properties, and fundamental bounds.

Main Methods:

  • Variational Matrix Product State (VMPS) techniques were employed.
  • The study focused on analyzing quasiparticle dispersion relations.
  • Numerical simulations were performed to probe excitation properties.

Main Results:

  • The local quasiparticle ansatz accurately describes excitations, even with large correlation lengths.
  • Topologically nontrivial excitations, such as spinons, are well-captured.
  • The breaking of the Lieb-Robinson bound is linked to cusps in the dispersion relation.
  • Evidence for a crossover between different quasiparticles was observed as interactions were tuned.

Conclusions:

  • The local quasiparticle ansatz is a robust tool for studying complex quantum systems.
  • Long-range interactions lead to distinct excitation behaviors and can violate standard bounds.
  • The findings provide insights into the fundamental properties of quantum spin chains.