Density Matrix Renormalization Group Approach to Nonequilibrium Phenomena

The density matrix renormalization group (DMRG) is a very accurate numerical technique developed to study strongly correlated many-body problems. A pedagogical exposition of the DMRG is provided, stressing its multiscaling character and the importance of a careful selection of the relevant degrees of freedom. The extension of the method to nonequilibrium phenomena is presented, and a probabilistic reaction-diffusion system is chosen as a relevant and didactically appropriate example of an application.

[1]  On the choice of the density matrix in the stochastic TMRG , 2001, cond-mat/0106194.

[2]  O. Seeberg.  Statistical Mechanics. — A Set of Lectures , 1975 .

[3]  A. Schadschneider,et al.  Stochastic light-cone CTMRG: a new DMRG approach to stochastic models , 2002 .

[4]  S. Rommer,et al.  CLASS OF ANSATZ WAVE FUNCTIONS FOR ONE-DIMENSIONAL SPIN SYSTEMS AND THEIR RELATION TO THE DENSITY MATRIX RENORMALIZATION GROUP , 1997 .

[5]  J. Zittartz,et al.  LETTER TO THE EDITOR: Transfer-matrix density-matrix renormalization group for stochastic models: the Domany-Kinzel cellular automaton , 2001 .

[6]  José A. González.  Quantum Electron Liquids and High-Tc Superconductivity , 1995 .

[7]  William H. Press,et al.  Numerical recipes in C , 2002 .

[8]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[9]  The correlated block renormalization group , 1995, cond-mat/9512130.

[10]  T. Nishino,et al.  Transfer-matrix approach to classical systems , 1999 .

[11]  N. Goldenfeld.  Lectures On Phase Transitions And The Renormalization Group , 1972 .

[12]  Density-matrix renormalization-group study of excitons in dendrimers , 2000, cond-mat/0012382.

[13]  R. Zwanzig.  Nonequilibrium statistical mechanics , 2001, Physics Subject Headings (PhySH).

[14]  Application of the Density Matrix Renormalization Group Methodto a Non-Equilibrium Problem , 1997, cond-mat/9711072.

[15]  L. Kadanoff.  Scaling laws for Ising models near T(c) , 1966 .

[16]  John B. Kogut,et al.  An introduction to lattice gauge theory and spin systems , 1979 .

[17]  A. Barabasi,et al.  Fractal concepts in surface growth , 1995 .

[18]  M. Henkel,et al.  Density matrix renormalization group and reaction-diffusion processes , 1999, cond-mat/9902041.

[19]  Generalized contact process with n absorbing states. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Critical properties of the reaction-diffusion model 2A-->3A, 2A-->0. , 1999, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  A. Fisher,et al.  The Theory of critical phenomena , 1992 .

[22]  Real Space Renormalization Group Techniques and Applications , 2002, cond-mat/0207340.

[23]  G. Sierra,et al.  Russian doll renormalization group and Kosterlitz–Thouless flows , 2003 .

[24]  White,et al.  Density matrix formulation for quantum renormalization groups. , 1992, Physical review letters.

[25]  A non-perturbative real-space renormalization group scheme , 1999, cond-mat/9910511.

[26]  M. Suzuki,et al.  Relationship between d-Dimensional Quantal Spin Systems and (d+1)-Dimensional Ising Systems: Equivalence, Critical Exponents and Systematic Approximants of the Partition Function and Spin Correlations , 1976 .

[27]  Karen Hallberg.  Density Matrix Renormalization , 1999 .

[28]  G. Schütz.  1 – Exactly Solvable Models for Many-Body Systems Far from Equilibrium , 2001 .

[29]  White,et al.  Density-matrix algorithms for quantum renormalization groups. , 1993, Physical review. B, Condensed matter.

[30]  Pair contact process with diffusion: anew type of nonequilibrium critical behavior? , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  White,et al.  Real-space quantum renormalization groups. , 1992, Physical review letters.

[32]  K. Wilson.  The renormalization group: Critical phenomena and the Kondo problem , 1975 .