Pair Approximating the Action For Molecular Rotations in Path Integral Monte Carlo

Abstract

Typical path integral Monte Carlo approaches use the primitive approximation to compute the probability density for a given path. In this work, we develop the pair Discrete Variable Representation (pair-DVR) approach to study molecular rotations. The pair propagator, which was initially introduced to study superfluidity in condensed Helium, is naturally well-suited for systems interacting with a pair-wise potential. Consequently, paths sampled using the pair action tend to be closer to the exact paths (compared to primitive Trotter paths) for such systems leading to convergence with less imaginary time steps. Therefore, our approach relies on using the pair factorization approach in conjunction with a discretized Path Integral Ground State (PIGS) paradigm to study a chain of planar rotors interacting with a pair-wise dipole interaction. We first use the Wigner-Kirkwood density expansion to analyze the asymptotics of the pair propagator in imaginary time. Then, we exhibit the utility of the pair factorization scheme via convergence studies comparing the pair and primitive propagators. Finally, we compute energetic and structural properties of this system including the correlation function and Binder ratio as functions of the coupling strength to examine the behaviour of the pair-DVR method near criticality. Density Matrix Renormalization Group results are used for benchmarking throughout.

References in corpus (13)

• Cold and Ultracold Molecules: Science, Technology, and Applications
• The ITensor Software Library for Tensor Network Calculations
• Realizing a lattice spin model with polar molecules
• On-Demand Entanglement of Molecules in a Reconfigurable Optical Tweezer Array
• Exact quantum Monte Carlo study of one dimensional trapped fermions with attractive contact interactions
• Topological critical slowing down: variations on a toy model
• Path integral Monte Carlo ground state approach: Formalism, implementation, and applications
• Incorporating exact two-body propagators for zero-range interactions into $N$-body Monte Carlo simulations
• Efficient Irreversible Monte Carlo samplers
• Contact interaction in an unitary ultracold Fermi gas
• Quantum phases of dipolar rotors on two-dimensional lattices
• Quantum criticality in chains of planar rotors with dipolar interactions
• Path integral Monte Carlo in a discrete variable representation with Gibbs sampling: dipolar planar rotor chain

Cited by in corpus (2)

• Path Integral Monte Carlo in the Angular Momentum Basis for a Chain of Planar Rotors
• Qubit encodings for lattices of dipolar planar rotors