Systematic errors in Gaussian Quantum Monte Carlo and a systematic study of the symmetry projection method

Abstract

Gaussian Quantum Monte Carlo (GQMC) is a stochastic phase space method for fermions with positive weights. In the example of the Hubbard model close to half filling it fails to reproduce all the symmetries of the ground state leading to systematic errors at low temperatures. In a previous work [Phys. Rev. B {\bf 72}, 224518 (2005)] we proposed to restore the broken symmetries by projecting the density matrix obtained from the simulation onto the ground state symmetry sector. For ground state properties, the accuracy of this method depends on a {\it large overlap} between the GQMC and exact density matrices. Thus, the method is not rigorously exact. We present the limits of the approach by a systematic study of the method for 2 and 3 leg Hubbard ladders for different fillings and on-site repulsion strengths. We show several indications that the systematic errors stem from non-vanishing boundary terms in the partial integration step in the derivation of the Fokker-Planck equation. Checking for spiking trajectories and slow decaying probability distributions provides an important test of the reliability of the results. Possible solutions to avoid boundary terms are discussed. Furthermore we compare results obtained from two different sampling methods: Reconfiguration of walkers and the Metropolis algorithm.

11 pages, 14 figures, revised version, new title

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• The density-matrix renormalization group
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Power Laws are Logarithmic Boltzmann Laws
• The Non-Abelian Density Matrix Renormalization Group Algorithm
• Power-law tails from multiplicative noise
• Gaussian quantum Monte Carlo methods for fermions
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• Gaussian phase-space representations for fermions
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• Symmetry projection schemes for Gaussian Monte Carlo methods

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• Stochastic simulations of fermionic dynamics with phase-space representations
• Impact ionization and multiple photon absorptions in the two-dimensional photoexcited Hubbard model
• The Nonequilibrium Many-Body Problem as a paradigm for extreme data science
• Phaseless quantum Monte-Carlo approach to strongly correlated superconductors with stochastic Hartree-Fock-Bogoliubov wavefunctions
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