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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...
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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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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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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Elementary excitations in gapped quantum spin systems.

Jutho Haegeman1, Spyridon Michalakis, Bruno Nachtergaele

  • 1Department of Physics and Astronomy, Ghent University, B-9000 Ghent, Belgium.

Physical Review Letters
|September 10, 2013
PubMed
Summary
This summary is machine-generated.

Quantum lattice systems with energy gaps can approximate specific eigenstates using local operators. This approximation

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Quantum information science

Background:

  • The Lieb-Robinson bound is crucial for understanding causality and dynamics in quantum lattice systems with local interactions.
  • Energy gaps in the spectrum of quantum systems are key to proving many theoretical results, especially concerning stability and localization.

Purpose of the Study:

  • To demonstrate that specific energy and momentum eigenstates in translationally invariant quantum lattice systems can be approximated.
  • To establish an exponential bound on the approximation error, dependent on the locality of the operator and spectral gaps.

Main Methods:

  • Constructing momentum superpositions of local operators acting on the ground state.
  • Analyzing the error of this approximation using the spectral gap above and below the target eigenvalue.
  • Explicitly applying the method to the Affleck-Kennedy-Lieb-Tasaki model.

Main Results:

  • Simultaneous energy and momentum eigenstates, separated in their momentum sector, can be arbitrarily well approximated.
  • The approximation error decays exponentially with the size of the local operator's support.
  • The rate of this exponential decay is determined by the energy gaps surrounding the target eigenvalue.

Conclusions:

  • The study provides a powerful technique for approximating specific eigenstates in gapped quantum lattice systems.
  • The findings have implications for quantum simulation, error correction, and understanding the dynamics of quantum many-body systems.
  • Generalizations and applications to other quantum models are discussed, highlighting the broad applicability of the method.