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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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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:
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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Quantum Criticality of Two-Dimensional Quantum Magnets with Long-Range Interactions.

Sebastian Fey1, Sebastian C Kapfer1, Kai Phillip Schmidt1

  • 1Lehrstuhl für Theoretische Physik I, Staudtstraße 7, Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany.

Physical Review Letters
|April 24, 2019
PubMed
Summary

We investigated quantum magnets with long-range interactions, finding that unfrustrated systems transition from mean-field to nearest-neighbor universality. Frustrated systems on a square lattice maintain nearest-neighbor universality, while triangular lattices may exhibit first-order transitions.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Magnetism
  • Statistical Mechanics

Background:

  • Quantum magnets exhibit critical phenomena governed by interactions.
  • Long-range interactions can significantly alter magnetic phase transitions.
  • Understanding universality classes is key to classifying critical behavior.

Purpose of the Study:

  • To study the critical breakdown of two-dimensional quantum magnets.
  • To investigate the effects of algebraically decaying long-range interactions.
  • To analyze the transverse-field Ising model on square and triangular lattices.

Main Methods:

  • Combining perturbative continuous unitary transformations with classical Monte Carlo simulations.
  • Extracting high-order series for one-particle excitations.
  • Analyzing the high-field quantum paramagnet phase.

Main Results:

  • Unfrustrated systems transition from mean-field to nearest-neighbor universality with continuously varying critical exponents.
  • Frustrated systems on the square lattice remain in the nearest-neighbor universality class, irrespective of interaction range.
  • Quantum criticality on the triangular lattice appears to be terminated by a first-order phase transition line.

Conclusions:

  • Long-range interactions can drive significant changes in universality classes for quantum magnets.
  • Lattice frustration plays a crucial role in determining the impact of long-range interactions.
  • The study provides insights into the complex phase diagrams of frustrated quantum magnetic systems.