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Optimal nonlinear passage through a quantum critical point.

Roman Barankov1, Anatoli Polkovnikov

  • 1Department of Physics, Boston University, Boston, Massachusetts 02215, USA.

Physical Review Letters
|September 4, 2008
PubMed
Summary
This summary is machine-generated.

Minimize defects during quantum critical point passage by tuning parameters via a power law. The optimal power depends on passage time and critical exponents for quantum phase transitions.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Statistical Mechanics

Background:

  • Quantum phase transitions (QPTs) are fundamental to understanding many-body quantum systems.
  • Adiabatic passage through a QPT is crucial for preparing specific quantum states.
  • Defect formation during passage can disrupt desired quantum states.

Purpose of the Study:

  • To determine the optimal strategy for traversing a quantum critical point with minimal defect creation.
  • To identify the relationship between tuning parameter dynamics and defect density.
  • To provide a general framework applicable to various quantum critical phenomena.

Main Methods:

  • Analysis of the Landau-Zener-Stückelberg perturbation theory in the context of QPTs.
  • Development of a scaling theory for defect formation during adiabatic passage.
  • Explicit numerical and analytical calculations for the transverse-field Ising model.

Main Results:

  • Optimal passage through a quantum critical point follows a power-law temporal dependence of the tuning parameter.
  • The optimal power-law exponent is determined by the logarithm of the total passage time and universal critical exponents.
  • The transverse-field Ising model serves as a concrete example validating the general scaling analysis.

Conclusions:

  • Power-law tuning provides an optimal pathway to minimize defects across quantum critical points.
  • The findings offer a practical guideline for experimental control of quantum systems near criticality.
  • This work establishes a theoretical foundation for defect-free quantum state preparation in critical regimes.