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Ground state overlap and quantum phase transitions.

Paolo Zanardi1, Nikola Paunković

  • 1Institute for Scientific Interchange (ISI), Villa Gualino, Viale Settimio Severo 65, I-10133 Torino, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 10, 2006
PubMed
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We introduce a new method to detect quantum phase transitions using the overlap function between ground states. Critical regions in quantum systems are identified by extremal points of this overlap function.

Area of Science:

  • Quantum Mechanics
  • Condensed Matter Physics

Background:

  • Quantum phase transitions (QPTs) are fundamental changes in the ground state of quantum systems.
  • Characterizing QPTs is crucial for understanding complex quantum phenomena.

Purpose of the Study:

  • To develop a novel characterization of quantum phase transitions.
  • To identify critical regions in quantum systems using the overlap function.

Main Methods:

  • Calculating the overlap function between ground states for varying external parameters.
  • Analyzing the extremal points of the overlap function and related functions.
  • Examining the Dicke and XY models as case studies.

Main Results:

  • Quantum criticality is precisely marked by the extremal points of the overlap function.

Related Experiment Videos

  • Demonstrated the effectiveness of the overlap function in identifying critical regions.
  • Established connections to Anderson orthogonality catastrophe and Loschmidt echo dynamics.

    • Conclusions:

    • The overlap function provides a robust tool for characterizing quantum phase transitions.
    • This approach offers new insights into the dynamics and fundamental properties of critical quantum systems.