Eur. Phys. J. B 12, 99-114 (1999)
https://doi.org/10.1007/s100510050983

Density matrix renormalization group and reaction-diffusion processes

¹ Laboratoire de Physique des Matériaux (Unité Mixte de Recherche CNRS No. 7556) , Université Henri Poincaré Nancy I, B.P. 239, 54506 Vandœuvre-lès-Nancy Cedex, France
² Sektion Physik, Ludwig-Maximilians-Universität München, Theresienstr. 37/III, 80333 München, Germany

Corresponding author: ^a carlon@lps.u-nancy.fr

Received: 2 February 1999
Published online: 15 November 1999

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 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 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.