Green’s function Monte Carlo study of SU(3) lattice gauge theory in(3+1)D

Abstract

A 'forward walking' Green's Function Monte Carlo algorithm is used to obtain expectation values for SU(3) lattice Yang-Mills theory in (3+1) dimensions. The ground state energy and Wilson loops are calculated, and the finitesize scaling behaviour is explored. Crude estimates of the string tension are derived, which agree with previous results at intermediate couplings; but more accurate results for larger loops will be required to establish scaling behaviour at weak coupling.

Monte Carlo Study of Glueball Masses in the Hamiltonian Limit of Su(3) Lattice Gauge Theory

“…One of the first attempts at such a calculation was performed using a Green's function MC approach pioneered by Hey and Stump for U(1) [24,25] and SU(2) [26] and later extended by Chin et al for SU (3) [27,28,29]. However the later investigations [30] showed that this approach requires the use of a "trial wave function" to guide random walkers in the ensemble towards the preferred regions of configuration space. This introduces a variational element into the procedure, in that the results may exhibit a systematic dependence on the trial wave function.…”

GREEN'S FUNCTION MONTE CARLO APPROACH TO SU(3) YANG-MILLS THEORY IN (3+1)D

“…That is certainly the pattern seen in the Euclidean calculations, or in the U(1) 2+1 model. 8 Unfortunately, however, our present results for the larger Wilson loops are not of sufficient accuracy to allow worthwhile estimates of R n for n ≥ 2.…”

“…1 Its application to the U(1) lattice gauge theory in (2+1)D was discussed by Hamer et al 8 It is implemented for an operator Q (assumed diagonal, for simplicity) by 6 recording the value Q(x i ) for each "ancestor" walker at the beginning of a measurement; propagating the ensemble as normal for J iterations, keeping a record of the "ancestor" of each walker in the current population; and taking the weighted average of the Q(x i ) with respect to the weights of the descendants of x i after the J iterations, using sufficient iterations J that the estimate reaches a 'plateau'.…”

SPECTRUM AND WAVE FUNCTIONS OF U(1)2+1 LATTICE GAUGE THEORY FROM MONTE CARLO HAMILTONIAN

“…The Hamiltonian formulation of the U(1) 2+1 model has been investigated using a variety of different methods. We can refer to the Quantum Monte Carlo methods [25][26][27][28], the projector Monte Carlo method [29,30], the ensemble projector Monte Carlo method [31], the Green's function Monte Carlo method [32], the Langevin technique [33] and the guided random walk method [34]. Furthermore, the model has been studied via the t-expansion method [35,36], the block renormalization group method [37], the correlated basis function method [38], the coupledcluster expansion [39,40], and series expansions [41,42].…”