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Quantum criticality for few-body systems: path-integral approach.

R A Sauerwein1, S Kais

  • 1Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 12, 2001
PubMed
Summary

We developed a path-integral method to study quantum phase transitions in few-body systems. This approach maps quantum problems to classical lattice models, revealing critical phenomena and interaction-driven transitions.

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Area of Science:

  • Quantum Mechanics
  • Statistical Physics
  • Condensed Matter Physics

Background:

  • Quantum phase transitions and critical phenomena are fundamental in many-body systems.
  • Few-body quantum systems offer a tractable platform for theoretical investigation.
  • Existing methods may face challenges in describing complex interactions and transitions.

Purpose of the Study:

  • To introduce a novel path-integral approach for analyzing quantum phase transitions.
  • To adapt the method for few-body quantum systems by discretizing spacetime.
  • To demonstrate its applicability in identifying critical points driven by interaction potentials.

Main Methods:

  • Discretization of space and time variables to transform quantum problems into classical lattice models.

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  • Imposing constraints on spacetime changes to preserve scaling invariance of Brownian paths.
  • Numerical evaluation of correlation length and radial mean distance for a specific potential.

    • Main Results:

    • The mapped classical lattice system exhibits known scaling behavior for free particles.
    • This scaling behavior breaks down when interaction potential strength reaches a critical value.
    • The transition point can be determined by observing deviations in scaling behavior.

    Conclusions:

    • The path-integral approach provides an effective framework for studying quantum phase transitions in few-body systems.
    • The method successfully identifies critical phenomena linked to interaction potential strength.
    • The approach is general and shows potential for application to larger, more complex quantum systems.