Light Front Ensemble Projector Mont Carlo

Abstract

A new method to perform numerical simulations of light-front Hamiltonians formulated on transverse lattices is introduced. The method is based on a DLCQ formulation for the (continuous) longitudinal directions. The hopping term in the transverse direction introduces couplings between fields defined on neighboring $1+1$-dimensional sheets. Within each sheet, the light-cone imaginary time evolution operator is calculated numerically with high precision using DLCQ. The coupling between neighboring sheets is taken into account using an initial value random walk algorithm based on the ensemble projector Monte Carlo technique and a checkerboard decomposition for the time evolution operator. The structure functions of $λϕ^4$ theory in $2+1$ dimensions are studied as a trial application. The calculations are performed with up to 64 transverse lattice sites. No Tamm-Dancoff truncations are necessary.