scholarly journals Green’s function Monte Carlo study of correlation functions in the(2+1)-dimensionalU(1)lattice gauge theory

2000 ◽  
Vol 62 (5) ◽  
Author(s):  
C. J. Hamer ◽  
R. J. Bursill ◽  
M. Samaras
Keyword(s):  
Monte Carlo ◽  
Gauge Theory ◽  
Green’S Function ◽  
Green's Function ◽  
Correlation Functions ◽  
Lattice Gauge Theory ◽  
Monte Carlo Study ◽  
Lattice Gauge ◽  
Green's Function Monte Carlo

scholarly journals The Use of Parameter-Free Correlation Functions in Green's Function Monte Carlo Simulations of Small Electronic Systems

1997 ◽  
Vol 52 (11) ◽  
pp. 793-802 ◽  
Author(s):  
C. Mecke ◽  
F. F. Seelig
Keyword(s):  
Monte Carlo ◽  
Green’S Function ◽  
Green's Function ◽  
Correlation Functions ◽  
High Performance ◽  
Limited Range ◽  
Electronic Energy ◽  
Simple Expression ◽  
Electronic Systems ◽  
Green's Function Monte Carlo

Abstract Using an old formulation for correlation functions with correct cusp-behaviour, the Schrödinger equation transforms to a new differential equation which provides a very simple expression for the local electronic energy with limited range. This, together with the simplicity of the formulation promises a high performance in Green's function Monte Carlo (GFMC) simulations of small electronic systems. The behaviour of the local energy is studied on a few simple examples because the variance of this function determines the quality of the results in the GFMC methods. Calculations for one-and two-electron systems are presented and compared with results from well-known functions. The form of the function is then extended to systems with more than two electrons. Results for the Be atom are given and the extension to larger electronic systems is discussed.

scholarly journals Forward-walking Green's Function Monte Carlo Method for Correlation Functions

1999 ◽  
Vol 52 (4) ◽  
pp. 637 ◽  
Author(s):  
M. Samaras ◽  
C. J. Hamer
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Green’S Function ◽  
Green's Function ◽  
Correlation Functions ◽  
Exact Results ◽  
Expectation Values ◽  
Trial Wavefunction ◽  
Local Observables ◽  
Green's Function Monte Carlo

The forward-walking Green's Function Monte Carlo method is used to compute expectation values for the transverse Ising model in (1 + 1)D, and the results are compared with exact values. The magnetisation Mz and the correlation function p z (n) are computed. The algorithm reproduces the exact results, and convergence for the correlation functions seems almost as rapid as for local observables such as the magnetisation. The results are found to be sensitive to the trial wavefunction, however, especially at the critical point.

scholarly journals MONTE CARLO STUDY OF GLUEBALL MASSES IN THE HAMILTONIAN LIMIT OF SU(3) LATTICE GAUGE THEORY

2006 ◽  
Vol 21 (13n14) ◽  
pp. 2905-2936 ◽  
Author(s):  
MUSHTAQ LOAN ◽  
XIANG-QIAN LUO ◽  
ZHI-HUAN LUO
Keyword(s):  
Monte Carlo ◽  
Gauge Theory ◽  
Lattice Spacing ◽  
Lattice Gauge Theory ◽  
Axial Vector ◽  
Accurate Determination ◽  
Monte Carlo Study ◽  
Euclidean Case ◽  
Reliable Technique ◽  
Lattice Gauge

Using Standard Euclidean Monte Carlo techniques, we discuss in detail the extraction of the glueball masses of four-dimensional SU(3) lattice gauge theory in the Hamiltonian limit, where the temporal lattice spacing is zero. By taking into account the renormalization of both the anisotropy and the Euclidean coupling, we calculate the string tension and masses of the scalar, axial vector and tensor states using standard Wilson action on increasingly anisotropic lattices, and make an extrapolation to the Hamiltonian limit. The results are compared with estimates from various other Hamiltonian and Euclidean studies. We find that more accurate determination of the glueball masses and the mass ratios has been achieved in the Hamiltonian limit and the results are a significant improvement upon previous Hamiltonian estimates. The continuum predictions are then found by extrapolation of results obtained from smallest values of spatial lattice spacing. For the lightest scalar, tensor and axial vector states we obtain masses of m0++ = 1654±83 MeV , m2++ = 2272±115 MeV and m1+- = 2940±165 MeV , respectively. These are consistent with the estimates obtained in the previous studies in the Euclidean limit. The consistency is a clear evidence of universality between Euclidean and Hamiltonian formulations. From the accuracy of our estimates, we conclude that the standard Euclidean Monte Carlo method is a reliable technique for obtaining results in the Hamiltonian version of the theory, just as in Euclidean case.

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