Path integral Monte Carlo in a discrete variable representation with Gibbs sampling: Dipolar planar rotor chain.

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.