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.

• Publication year

  1999

• Venue

  The European Physical Journal B - Condensed Matter and Complex Systems

• Publication date

  1999-02-03

• Fields of study

  Physics

• Identifiers
  DOI 10.1007/s100510050983arXiv cond-mat/9902041
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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