Stochastic Light-Cone CTMRG: a new DMRG approach to stochastic models

Abstract

We develop a new variant of the recently introduced stochastic transfer-matrix DMRG which we call stochastic light-cone corner-transfer-matrix DMRG (LCTMRG). It is a numerical method to compute dynamic properties of one-dimensional stochastic processes. As suggested by its name, the LCTMRG is a modification of the corner-transfer-matrix DMRG (CTMRG), adjusted by an additional causality argument. As an example, two reaction-diffusion models, the diffusion-annihilation process and the branch-fusion process, are studied and compared to exact data and Monte-Carlo simulations to estimate the capability and accuracy of the new method. The number of possible Trotter steps of more than 10^5 shows a considerable improvement to the old stochastic TMRG algorithm.

arXiv comment15 pages, uses IOP style

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Cited by in corpus (12)

• The density-matrix renormalization group
• Exploring corner transfer matrices and corner tensors for the classical simulation of quantum lattice systems
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• Dynamical simulations of classical stochastic systems using matrix product states
• Application of the density matrix renormalization group method to finite temperatures and two-dimensional systems
• Ageing phenomena without detailed balance: the contact process
• Optimal sampling of dynamical large deviations via matrix product states
• Construction of a matrix product stationary state from solutions of finite size system
• Quantum Scaling Approach to Nonequilibrium Models
• Holographic encoding of universality in corner spectra
• Thermodynamic properties and thermal correlation lengths of a Hubbard model with bond-charge interaction
• Tensor-Network Approaches to Counting Statistics for the Current in a Boundary-Driven Diffusive System