Stochastic Light-Cone CTMRG: a new DMRG approach to stochastic models

TL;DR

This paper introduces a novel stochastic light-cone corner-transfer-matrix DMRG method for efficiently computing dynamic properties of one-dimensional stochastic processes, demonstrating significant improvements over previous algorithms.

Contribution

It presents a new variant of stochastic TMRG, called LCTMRG, that incorporates causality to enhance accuracy and efficiency in modeling stochastic systems.

Findings

LCTMRG outperforms previous stochastic TMRG in Trotter steps

Accurately models reaction-diffusion processes

Shows good agreement with exact and Monte Carlo data

Abstract

We develop a new variant of the recently introduced stochastic transfer-matrix DMRG which we call stochastic light-cone corner-transfer-matrix DMRG (LCTMRG). It is a numerical method to compute dynamic properties of one-dimensional stochastic processes. As suggested by its name, the LCTMRG is a modification of the corner-transfer-matrix DMRG (CTMRG), adjusted by an additional causality argument. As an example, two reaction-diffusion models, the diffusion-annihilation process and the branch-fusion process, are studied and compared to exact data and Monte-Carlo simulations to estimate the capability and accuracy of the new method. The number of possible Trotter steps of more than 10^5 shows a considerable improvement to the old stochastic TMRG algorithm.