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Multilevel algorithm for quantum-impurity models.

Jaebeom Yoo1, Shailesh Chandrasekharan, Harold U Baranger

  • 1Department of Physics, Duke University, Durham, North Carolina 27708, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2005
PubMed
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A new quantum Monte Carlo method simulates the Anderson single-impurity model efficiently. A multilevel algorithm overcomes the sign problem, enabling accurate simulations at low temperatures for condensed matter physics research.

Area of Science:

  • Condensed Matter Physics
  • Computational Physics

Background:

  • The Anderson single-impurity model is crucial for understanding electron correlations in materials.
  • Simulating this model at low temperatures is computationally challenging due to the sign problem in quantum Monte Carlo methods.

Purpose of the Study:

  • To develop a novel continuous-time path integral quantum Monte Carlo method for the Anderson single-impurity model.
  • To address the sign problem and improve simulation efficiency.

Main Methods:

  • Implementation of a directed-loop algorithm in the occupation number basis.
  • Development and application of a multilevel algorithm to mitigate the sign problem.

Main Results:

  • The new method simulates the Kondo limit without time discretization errors.

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  • Efficient calculation of impurity susceptibility and fermionic observables is achieved.
  • The multilevel algorithm generates exponentially more positive-sign configurations with polynomial effort.

    • Conclusions:

    • The developed quantum Monte Carlo method offers significant advantages over conventional algorithms.
    • The multilevel algorithm provides an effective solution to the sign problem in quantum Monte Carlo simulations.
    • The approach is generalizable to multi-impurity systems.