Improved Multi-Variable Variational Monte Carlo Method Examined by High-Precision Calculations of One-Dimensional Hubbard Model

TL;DR

This paper enhances the variational Monte Carlo method for the one-dimensional Hubbard model by incorporating quantum-number projections and improved wave functions, achieving high accuracy in ground state energies and critical exponents.

Contribution

It introduces advanced quantum-number projections and generalized wave functions to significantly improve VMC accuracy for the Hubbard model.

Findings

Ground state energy accuracy within 0.5% error with projections

Accurate estimation of critical exponents matching Tomonaga-Luttinger theory

Effective method for large system sizes up to 196 sites

Abstract

We revisit the accuracy of the variational Monte Carlo (VMC) method by taking an example of ground state properties for the one-dimensional Hubbard model. We start from the variational wave functions with the Gutzwiller and long-range Jastrow factor introduced by Capello et al. [Phys. Rev. B 72, 085121 (2005)] and further improve it by considering several quantum-number projections and a generalized one-body wave function. We find that the quantum spin projection and total momentum projection greatly improve the accuracy of the ground state energy within 0.5% error, for both small and large systems at half filling. Besides, the momentum distribution function n(k) at quarter filling calculated up to 196 sites allows us direct estimate of the critical exponents of the charge correlations from the power-law behavior of n(k) near the Fermi wave vector. Estimated critical exponents well reproduce those predicted by the Tomonaga-Luttinger theory.