Density matrix renormalization group and reaction-diffusion processes

Carlon, Enrico; Henkel, Malte; Schollwöck, Ulrich

doi:10.1007/s100510050983

Cited by 100 publications

(130 citation statements)

References 28 publications

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“…The most famous of these approaches is certainly the density matrix renormalisation group (DMRG) [15,16]. This technique has by now been adapted to stochastic systems [17,18,19]. The method is asymptotic in time, but at this moment can treat only systems consisting of approximately 50-100 sites.…”

Section: Introductionmentioning

confidence: 99%

One-dimensional contact process: Duality and renormalization

Hooyberghs

Vanderzande

2001

Phys. Rev. E

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We study the one-dimensional contact process in its quantum version using a recently proposed real space renormalisation technique for stochastic many-particle systems. Exploiting the duality and other properties of the model, we can apply the method for cells with up to 37 sites. After suitable extrapolation, we obtain exponent estimates which are comparable in accuracy with the best known in the literature.

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Section: Introductionmentioning

confidence: 99%

One-dimensional contact process: Duality and renormalization

Hooyberghs

Vanderzande

2001

Phys. Rev. E

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“…In the limit ǫ → 0 we recover Equation (23), with λ → e −h . For the second order result (18) we require also the excited projection matrix E 1 = e ⊗N/2 1 and embedding matrix E 2 = e ⊗N/2 2 , which are determined by…”

Section: Rg For the Attractive East Modelmentioning

confidence: 99%

Two-stage coarsening mechanism in a kinetically constrained model of an attractive colloid

Whitelam

Geissler

2006

Phys. Rev. E

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We study an attractive version of the East model using the real-space renormalization group (RG) introduced by Stella et al. The former is a kinetically constrained model with an Ising-like interaction between excitations, and shows striking agreement with the phenomonology of attractive colloidal systems. We find that the RG predicts two nonuniversal dynamic exponents, which suggests that in the out-of-equilibrium regime the model coarsens via a two-stage mechanism. We explain this mechanism physically, and verify this prediction numerically. In addition, we predict that the characteristic relaxation time of the model is a non-monotonic function of attraction strength, again in agreement with numerical results.

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“…Applications of the TMRG for classical row transfer matrices include the two-dimensional Ising model [110], the spin-3/2 Ising model [113], wetting phenomena [114,115], the q-state Potts model [116], the q-state Potts model with random exchange [117], the 19-vertex model [118], and the three-state chiral clock model [119]. For a more extensive recent survey, see Ref.…”

Section: Classical Transfer Matricesmentioning

confidence: 99%

Diagonalization- and Numerical Renormalization-Group-Based Methods for Interacting Quantum Systems

Noack¹,

Manmana²

2005

AIP Conference Proceedings

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Abstract. In these lecture notes, we present a pedagogical review of a number of related numerically exact approaches to quantum many-body problems. In particular, we focus on methods based on the exact diagonalization of the Hamiltonian matrix and on methods extending exact diagonalization using renormalization group ideas, i.e., Wilson's Numerical Renormalization Group (NRG) and White's Density Matrix Renormalization Group (DMRG). These methods are standard tools for the investigation of a variety of interacting quantum systems, especially low-dimensional quantum lattice models. We also survey extensions to the methods to calculate properties such as dynamical quantities and behavior at finite temperature, and discuss generalizations of the DMRG method to a wider variety of systems, such as classical models and quantum chemical problems. Finally, we briefly review some recent developments for obtaining a more general formulation of the DMRG in the context of matrix product states as well as recent progress in calculating the time evolution of quantum systems using the DMRG and the relationship of the foundations of the method with quantum information theory.

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Density matrix renormalization group and reaction-diffusion processes

Abstract: PACS. 64.60.Ht Dynamic critical phenomena - 02.70.-c Computational techniques - 02.60.Dc Numerical linear algebra,

Cited by 100 publications

References 28 publications

One-dimensional contact process: Duality and renormalization

One-dimensional contact process: Duality and renormalization

Two-stage coarsening mechanism in a kinetically constrained model of an attractive colloid

Diagonalization- and Numerical Renormalization-Group-Based Methods for Interacting Quantum Systems

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