Efficient World-line-based Quantum Monte Carlo Method Without Hubbard-Stratonovich Transformation

TL;DR

This paper introduces a novel quantum Monte Carlo method that avoids the Hubbard-Stratonovich transformation, leading to improved efficiency and accuracy in simulating quantum systems, exemplified by the Hubbard model.

Contribution

A new path integral formulation and Monte Carlo algorithm that eliminate the need for Hubbard-Stratonovich transformation, enhancing computational efficiency and accuracy.

Findings

Simulation time scales quadratically with system size.

Results agree well with known solutions of the Hubbard model.

Improved accuracy in Suzuki-Trotter decomposition.

Abstract

By precisely writing down the matrix element of the local Boltzmann operator, we have proposed a new path integral formulation for quantum field theory and developed a corresponding Monte Carlo algorithm. With current formula, the Hubbard-Stratonovich transformation is not necessary, and is not based on the determinant approach, which can improve the computational efficiency. The results show that, the simulation time has the square-law scaling with system sizes, which is comparable with the usual first-principle calculation. The current formula also improves the accuracy of the Suzuki-Trotter decomposition. As an example, we have studied the one-dimensional half-filled Hubbard model at finite temperature. The obtained results are in excellent agreement with the known solutions. The new formula and Monte Carlo algorithm can be used in various studies.