1999/02/03 by Enrico Carlon, Malte Henkel, Ulrich Schollwöck +1 · 3 citations
Mathematics · Physics and Astronomy · #Critical exponent #Density matrix #Density matrix renormalization group #Directed percolation #Extrapolation #Geometry #Hamiltonian (control theory) #Mathematical analysis #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum many-body systems #Quantum mechanics #Renormalization group #Scaling #Statistical physics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1007/s100510050983
published as Eur.Phys.J.B12:99,1999 · 16 pages, latex, 5 PostScript figures included
arxiv created 1999/02/03 · openalex publication_date 1999/10/01 · arxiv updated 2011/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.