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A Complexity-Based Approach to Quantum Observable Equilibration.

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Quantum Statistical Complexity Measure as a Signaling of Correlation Transitions.

André T Cesário1, Diego L B Ferreira1, Tiago Debarba2

  • 1Departamento de Física, ICEx, Universidade Federal de Minas Gerais (UFMG), Av. Pres. Antônio Carlos 6627, Belo Horizonte 31270-901, Brazil.

Entropy (Basel, Switzerland)
|August 26, 2022
PubMed
Summary

We developed a quantum statistical complexity measure to detect quantum order-disorder transitions. This new tool helps identify quantum phase transitions and variations in quantum correlations.

Keywords:
1D-Quantum Ising ModelHeisenberg XXZ spin-1/2 Modelquantum phase transitionsquantum statistical complexity measurestatistical complexity measure

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Area of Science:

  • Quantum Information Theory
  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Statistical complexity quantifies the information needed to describe a system's state.
  • Quantum phase transitions represent abrupt changes in quantum systems at absolute zero temperature.
  • Understanding quantum correlations is crucial for characterizing complex quantum phenomena.

Purpose of the Study:

  • Introduce a quantum statistical complexity measure.
  • Utilize this measure as a signaling function for quantum order-disorder transitions.
  • Explore its application in identifying quantum phase transitions and correlation variations.

Main Methods:

  • Developed a quantum version of the statistical complexity measure.
  • Applied the measure to exactly solvable Hamiltonian models.
  • Analyzed behavior across quantum phase transitions using the Bethe Ansatz technique.

Main Results:

  • The quantum statistical complexity measure effectively signals quantum order-disorder transitions.
  • The measure's behavior was analyzed for finite and infinite system sizes.
  • Distinct signatures of quantum phase transitions were observed.

Conclusions:

  • The quantum statistical complexity measure is a valuable tool for detecting quantum phase transitions.
  • This approach provides insights into variations in quantum correlation distributions.
  • The study demonstrates the measure's efficacy in exactly solvable models.