Light Front Ensemble Projector Mont Carlo

TL;DR

This paper introduces a novel numerical simulation method for light-front Hamiltonians on transverse lattices, combining DLCQ and ensemble projector Monte Carlo techniques to study quantum field theories without Tamm-Dancoff truncations.

Contribution

The paper presents a new computational approach integrating DLCQ and Monte Carlo methods for light-front Hamiltonian simulations on transverse lattices.

Findings

Successfully simulated $mbda \u00b4phi^4$ theory in 2+1 dimensions

Achieved high-precision calculations with up to 64 lattice sites

Eliminated the need for Tamm-Dancoff truncations

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 $\lambda \phi^4$ 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.