arXiv subjects

Ulrich Schollwoeck

Publications and source records attributed to Ulrich Schollwoeck.

20 records · Page 2Linked to original sources

arXiv2000

Critical properties of the reaction - diffusion model 2A -> 3A, 2A ->0

The steady-state phase diagram of the one-dimensional reaction-diffusion model 2A -> 3A, 2A -> 0 is studied through the non-hermitian density matrix renormalization group. In the absence of single-particle diffusion the model reduces to the pair-contact process, which has a phase transition in the universality class of Directed Percolation (DP) and an infinite number of absorbing steady states. When single-particle diffusion is added, the number of absorbing steady states is reduced to two and the model does not show DP critical behaviour anymore. The exponents $θ=ν_{\|}/ν_{\perp}$ and $β/ν_{\perp}$ are calculated numerically. The value of $β/ν_{\perp}$ is close to the value of the Parity Conserving universality class, in spite of the absence of local conservation laws.

cond-mat.stat-mech↗

arXiv1999

Density Matrix Renormalization Group and Reaction-Diffusion Processes

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.

cond-mat.stat-mech↗