Application of The Density Matrix Renormalization Group Algorithm to Classical Driven Diffusive Systems in One and Two Dimensions

The Density Matrix Renormalization Group (DMRG) algorithm is recognized as one of the most accurate quantum chemistry methods for calculations involving strongly-correlated particles. Its utility has recently been expanded from quantum systems to classical non-equilibrium systems such as the Symmetric Exclusion Process (SEP), which fall into the category of driven diffussive systems. Here, I first introduce the DMRG algorithm from the Matrix Product States paradigm and describe how it can be used to calculate the steady-state properties of the SEP in one and two dimensions. Last, the phase behavior of the SEP is discussed in both dimensions with comparison to analytic solutions and Monte Carlo calculations.