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Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
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Schottky defects arise when some lattice points in a crystal, such as those in NaCl, remain unoccupied, creating lattice vacancies without disturbing the overall electrical neutrality of the crystal. This defect is common in ionic crystals where the positive and negative ions are similar in size, as seen in sodium chloride and cesium chloride. The presence of Schottky defects enables the crystal to conduct electricity to a small extent through an ionic mechanism. Electric fields cause nearby...
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The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
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Updated: Mar 24, 2026

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Correlation Length versus Gap in Frustration-Free Systems.

David Gosset1,2, Yichen Huang2

  • 1Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA.

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|March 19, 2016
PubMed
Summary
This summary is machine-generated.

Frustration-free quantum systems exhibit slower correlation decay near criticality than previously thought. We prove a new tight bound for correlation length scaling with the spectral gap in these systems.

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Area of Science:

  • Quantum Many-Body Physics
  • Condensed Matter Theory
  • Statistical Mechanics

Background:

  • Hastings' theorem established exponential decay of correlations for gapped quantum many-body systems.
  • The correlation length (ξ) of local Hamiltonians with spectral gap (ε) is bounded by ξ=O(1/ε).
  • This bound is generally tight, but its applicability to specific system types remains an area of study.

Purpose of the Study:

  • To investigate the scaling of correlation length with the spectral gap in frustration-free local Hamiltonians.
  • To determine if a tighter bound exists for correlation length in frustration-free systems compared to general gapped systems.
  • To understand the implications of frustration-free conditions on system criticality.

Main Methods:

  • Utilizing an improved combinatorial proof for correlation decay.
  • Adapting techniques from Aharonov, Arad, Vazirani, and Landau.
  • Analyzing the properties of ground states in frustration-free local Hamiltonians.

Main Results:

  • A new tight bound for correlation length scaling in frustration-free systems is proven: ξ=O(1/√ε).
  • This bound demonstrates a slower decay of correlations compared to the general ξ=O(1/ε) bound.
  • A fundamental difference in behavior near criticality between frustration-free and frustrated systems is highlighted.

Conclusions:

  • The frustration-free condition allows for a distinct, slower correlation decay scaling with the spectral gap.
  • The established bound ξ=O(1/√ε) is tight for frustration-free local Hamiltonians.
  • This finding offers new insights into the critical behavior of quantum many-body systems.