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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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In the field of psychology, there are several ways to organize measurements of a trait, feature, or characteristic (i.e., variables). Qualitative data, such as ethnicity, can be tabulated into a frequency count to provide information about the proportion, as well as the variety of groups in a sample or population. On the other hand, researchers can perform a wider set of calculations on quantitative data. The mean, mode, and median, for instance, are central tendency measures to identify a...
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Associated Chromosome Trap for Identifying Long-range DNA Interactions
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Topological phases with long-range interactions.

Z-X Gong1,2, M F Maghrebi1,2, A Hu1,3

  • 1Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA.

Physical Review. B
|July 6, 2019
PubMed
Summary
This summary is machine-generated.

Topological phases of matter can survive long-range interactions if they are frustrated. Unfrustrated interactions destroy these phases, but frustrated interactions preserve them for all interaction strengths.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Materials Science

Background:

  • Topological phases of matter are typically studied in systems with short-range interactions.
  • Real-world quantum systems often feature long-range interactions, but their effect on topological phases is poorly understood.

Purpose of the Study:

  • Investigate the survival and modification of symmetry-protected topological phases under long-range interactions.
  • Determine the conditions under which topological phases persist in systems with 1/r^α interactions.

Main Methods:

  • Studied an antiferromagnetic spin-1 chain model with 1/r^α interactions.
  • Employed large-scale matrix-product-state simulations.
  • Conducted effective-field-theory calculations.

Main Results:

  • Discovered two distinct outcomes for topological phases depending on interaction frustration.
  • Unfrustrated long-range interactions destroy topological phases for α ≲ 3.
  • Frustrated interactions preserve topological phases for all α > 0.

Conclusions:

  • Topological phase survival is critically dependent on interaction frustration.
  • Findings are consistent across simulations and theoretical calculations.
  • The studied models are realizable in trapped-ion quantum simulators for experimental verification.