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Cluster Monte Carlo algorithm for the quantum rotor model.

Fabien Alet1, Erik S Sørensen

  • 1Laboratoire de Physique Quantique and UMR 5626, Université Paul Sabatier, 31062 Toulouse, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 15, 2003
PubMed
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We developed an efficient Monte Carlo algorithm for the quantum rotor model. This new method accurately determines critical points and correlation exponents for both pure and disordered systems.

Area of Science:

  • Condensed matter physics
  • Computational physics

Background:

  • The quantum rotor model is a fundamental model in statistical mechanics.
  • Efficient algorithms are crucial for studying phase transitions in quantum systems.

Purpose of the Study:

  • To introduce a novel, highly efficient "worm"-like cluster Monte Carlo algorithm.
  • To apply this algorithm to the quantum rotor model in the link-current representation.
  • To rigorously prove the algorithm's detailed balance, even with disorder.

Main Methods:

  • Development of a "worm"-like cluster Monte Carlo algorithm.
  • Application to the quantum rotor model in the link-current representation.
  • Explicit proof of detailed balance for the algorithm.

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Main Results:

  • High-precision estimation of the critical point K(c)=0.333 05(5) for the pure quantum rotor model (mu=0).
  • Accurate determination of the correlation length exponent nu=0.670(3) for the pure model.
  • Determination of the correlation length exponent nu=1.15(10) for the disordered case (mu=1/2 +/- 1/2).

Conclusions:

  • The proposed algorithm is highly efficient for the quantum rotor model.
  • The algorithm accurately handles both pure and disordered systems.
  • Provides precise critical parameters for the quantum rotor model.