Density Matrix Renormalization Group and Reaction-Diffusion Processes

Abstract

The density matrix renormalization group (DMRG) is applied to some one-dimensional reaction-diffusion models in the vicinity of and at their critical point. The stochastic time evolution for these models is given in terms of a non-symmetric ``quantum Hamiltonian'', which is diagonalized using the DMRG method for open chains of moderate lengths (up to about 60 sites). The numerical diagonalization methods for non-symmetric matrices are reviewed. Different choices for an appropriate density matrix in the non-symmetric DMRG are discussed. Accurate estimates of the steady-state critical points and exponents can then be found from finite-size scaling through standard finite-lattice extrapolation methods. This is exemplified by studying the leading relaxation time and the density profiles of diffusion-annihilation and of a branching-fusing model in the directed percolation universality class.