Application of the Green's function Monte Carlo method to Hamiltonian lattice field theories

We present a general formulation of the Green's function Monte Carlo method in imaginary-time quantum Monte Carlo which employs exact propagators. This algorithm has no time-step errors and is obtained by minimal modifications of the time-independent Green's function Monte Carlo method. We describe how the method can be applied to the many-body Schrödinger equation, lattice Hamiltonians, and simple field theories. Our modification of the Green's function Monte Carlo algorithm is applied to the ground state of liquid 4He. We calculate the zero-temperature imaginary-time diffusion constant and relate that to the effective mass of a mass-four "impurity" atom in liquid 4He.We present a general formulation of the Green's function Monte Carlo method in imaginary-time quantum Monte Carlo which employs exact propagators. This algorithm has no time-step errors and is obtained by minimal modifications of the time-independent Green's function Monte Carlo method. We describe how the method can be applied to the many-body Schrödinger equation, lattice Hamiltonians, and simple field theories. Our modification of the Green's function Monte Carlo algorithm is applied to the ground state of liquid 4He. We calculate the zero-temperature imaginary-time diffusion constant and relate that to the effective mass of a mass-four "impurity" atom in liquid 4He.

Physical Review EJan 1, 200544 citations

Application of the Green's-function Monte Carlo method to the Hamiltonian XY model

David W. Heys, Daniel R. Stump

An application of the Green's-function Monte Carlo method to the Hamiltonian $\mathrm{XY}$ model is described. Importance sampling is implemented with two trial wave functions---one corresponding to a disordered state and one which incorporates the correlations derived from the spin-wave approximation of the model. Optimal trial functions are obtained from the variational principle. The Monte Carlo results are interpreted with regard to the Kosterlitz-Thouless phase transition.An application of the Green's-function Monte Carlo method to the Hamiltonian $\mathrm{XY}$ model is described. Importance sampling is implemented with two trial wave functions---one corresponding to a disordered state and one which incorporates the correlations derived from the spin-wave approximation of the model. Optimal trial functions are obtained from the variational principle. The Monte Carlo results are interpreted with regard to the Kosterlitz-Thouless phase transition.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsApr 15, 19846 citations

Linearized auxiliary fields Monte Carlo technique: Efficient sampling of the fermion sign

Sandro Sorella

We introduce a method that combines the power of both the lattice Green' function Monte Carlo (LGFMC) with the auxiliary field quantum Monte Carlo (AFQMC) techniques, and allows us to compute exact ground-state properties of the Hubbard model for $U\ensuremath{\lesssim}4t$ on finite clusters. Thanks to LGFMC, one obtains unbiased zero temperature results, not affected by the so-called Trotter approximation of the imaginary time propagator ${e}^{\ensuremath{-}H\ensuremath{\tau}}$. At the same time, the AFQMC formalism yields a remarkably fast convergence in $\ensuremath{\tau}$ before the fermion sign problem becomes prohibitive. As an application we report ground-state energies of the Hubbard model at $U/t=4$ with up to 100 sites.We introduce a method that combines the power of both the lattice Green' function Monte Carlo (LGFMC) with the auxiliary field quantum Monte Carlo (AFQMC) techniques, and allows us to compute exact ground-state properties of the Hubbard model for $U\ensuremath{\lesssim}4t$ on finite clusters. Thanks to LGFMC, one obtains unbiased zero temperature results, not affected by the so-called Trotter approximation of the imaginary time propagator ${e}^{\ensuremath{-}H\ensuremath{\tau}}$. At the same time, the AFQMC formalism yields a remarkably fast convergence in $\ensuremath{\tau}$ before the fermion sign problem becomes prohibitive. As an application we report ground-state energies of the Hubbard model at $U/t=4$ with up to 100 sites.

arXiv:1111.6208Physical Review BDec 29, 201124 citations

An application of the Green's-function Monte Carlo method to the Hamiltonian

\mathrm{XY}

model is described. Importance sampling is implemented with two trial wave functions---one corresponding to a disordered state and one which incorporates the correlations derived from the spin-wave approximation of the model. Optimal trial functions are obtained from the variational principle. The Monte Carlo results are interpreted with regard to the Kosterlitz-Thouless phase transition.

U/t=4

with up to 100 sites.