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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
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.
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.
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