A DMRG study of the -symmetric Heisenberg chain

Kaulke, M.; Peschel, Ingo

doi:10.1007/s100510050496

Cited by 41 publications

(60 citation statements)

References 31 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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“…The method is most succesfull in one dimension. Given the formal similarity between quantum systems and stochastic ones, several groups started to apply this technique to interacting particle systems in recent years 23,45 . The method is now known to work well also in these cases though it cannot give as accurate results as for the spin chains, mainly because at this moment algorithms to diagonalise nonhermitean matrices are not as well developped as those for the hermitean case.…”

Section: Dmrg Studiesmentioning

confidence: 99%

“…In this study we make use of the formal analogy between quantum systems and the "Hamiltonian" operator formalism 20,21 of stochastic processes. Although the latter operators are generally non-hermitian, techniques developed in the study of quantum spin systems can often be successfully applied 21,22,23,24 . In the theory of random quantum spin systems, recently considerable progress has been made in understanding their low-energy (or long time), long distance behavior.…”

Section: Introductionmentioning

confidence: 99%

Absorbing state phase transitions with quenched disorder

2004

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Quenched disorder -in the sense of the Harris criterion -is generally a relevant perturbation at an absorbing state phase transition point. Here using a strong disorder renormalization group framework and effective numerical methods we study the properties of random fixed points for systems in the directed percolation universality class. For strong enough disorder the critical behavior is found to be controlled by a strong disorder fixed point, which is isomorph with the fixed point of random quantum Ising systems. In this fixed point dynamical correlations are logarithmically slow and the static critical exponents are conjecturedly exact for one-dimensional systems. The renormalization group scenario is confronted with numerical results on the random contact process in one and two dimensions and satisfactory agreement is found. For weaker disorder the numerical results indicate static critical exponents which vary with the strength of disorder, whereas the dynamical correlations are compatible with two possible scenarios. Either they follow a power-law decay with a varying dynamical exponent, like in random quantum systems, or the dynamical correlations are logarithmically slow even for weak disorder. For models in the parity conserving universality class there is no strong disorder fixed point according to our renormalization group analysis.

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“…Kaulke and Peschel [36] used the DMRG to study biased diffusion, which leads to a q-symmetric Hamiltonian H which is similar to a symmetric matrix. The feasibility of the Hamiltonian approach using the DMRG for truly non-equilibrium systems without detailed balance was demonstrated with E. Carlon and U. Schollwöck, on a model in the DP class [37].…”

Section: Introduction and Historymentioning

confidence: 99%

The non-equilibrium phase transition of the pair-contact process with diffusion

Henkel

Hinrichsen

2004

J. Phys. A: Math. Gen.

107

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Abstract. The pair-contact process 2A → 3A, 2A → ∅ with diffusion of individual particles is a simple branching-annihilation processes which exhibits a phase transition from an active into an absorbing phase with an unusual type of critical behaviour which had not been seen before. Although the model has attracted considerable interest during the past few years it is not yet clear how its critical behaviour can be characterized and to what extent the diffusive pair-contact process represents an independent universality class. Recent research is reviewed and some standing open questions are outlined.

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A DMRG study of the -symmetric Heisenberg chain

Cited by 41 publications

References 31 publications

One-dimensional contact process: Duality and renormalization

One-dimensional contact process: Duality and renormalization

Absorbing state phase transitions with quenched disorder

The non-equilibrium phase transition of the pair-contact process with diffusion

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