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We introduce a novel path integral Monte Carlo method using Gibbs sampling for studying quantum systems. This approach offers lower variance and correlation for observables compared to traditional sampling techniques.

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Area of Science:

  • Computational Physics
  • Quantum Mechanics
  • Statistical Mechanics

Background:

  • Path integral Monte Carlo (PIMC) methods are crucial for simulating quantum systems.
  • Traditional sampling techniques like Metropolis-Hastings can suffer from high variance and correlations.

Purpose of the Study:

  • To develop and validate a new PIMC approach utilizing Gibbs sampling.
  • To assess the efficiency and accuracy of this method for ground state properties of interacting rotors.

Main Methods:

  • Discretized continuous degrees of freedom with rejection-free Gibbs sampling.
  • Comparison with exact diagonalization and Density Matrix Renormalization Group (DMRG) for benchmarking.
  • Calculation of energetic and structural properties for planar rotor chains.

Main Results:

  • The proposed Gibbs sampling PIMC method demonstrates reduced variance and correlation in observables.
  • Accurate ground state properties were computed for chains of up to 100 rotors.
  • Systematic convergence of Trotter factorization error was assessed.

Conclusions:

  • Gibbs sampling offers a significant advantage over Metropolis-Hastings for PIMC simulations.
  • The new method provides an efficient and accurate tool for studying quantum many-body systems.
  • This approach is well-suited for investigating ground state properties of systems with continuous degrees of freedom.