The density-matrix renormalization group

DOI10.1103/RevModPhys.77.259zbMath1205.82073arXivcond-mat/0409292WikidataQ27349438 ScholiaQ27349438MaRDI QIDQ3077084

Ulrich Schollwöck

Publication date: 21 February 2011

Published in: Reviews of Modern Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/cond-mat/0409292

Mathematics Subject Classification ID

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Reaction-diffusion processes, critical dynamics, and quantum chains
• The density matrix renormalization group method applied to interaction round face Hamiltonians
• On the distribution of eigenvalues of grand canonical density matrices
• Relaxation times in the ASEP model using a DMRG method
• Corner Transfer Matrix Renormalization Group Method
• Corner Transfer Matrix Algorithm for Classical Renormalization Group
• Critical Properties of a Spin-3/2 Ising Model on a Square Lattice
• Application of the Density Matrix Renormalization Group Method to a Non-Equilibrium Problem
• Fixed Point of the Finite System DMRG
• Transfer-matrix density-matrix renormalization group for stochastic models: the Domany-Kinzel cellular automaton
• Universal finite-size scaling amplitudes in anisotropic scaling
• 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
• On the choice of the density matrix in the stochastic TMRG
• Two-Dimensional Tensor Product Variational Formulation
• Information and computation: Classical and quantum aspects
• On the Product of Semi-Groups of Operators
• ANGULAR QUANTIZATION AND THE DENSITY MATRIX RENORMALIZATION GROUP
• `Real' versus `imaginary' noise in diffusion-limited reactions
• Flow‐equations for Hamiltonians
• Numerical renormalization approach to two-dimensional quantum antiferromagnets with valence-bond-solid type ground state
• Application of the density matrix renormalization group method to finite temperatures and two-dimensional systems
• Quantum correlations and number theory
• Stochastic light-cone CTMRG: a new DMRG approach to stochastic models
• A corner transfer matrix renormalization group investigation of the vertex-interacting self-avoiding walk model
• First-Order Phase Transition in theS=1Quantum Spin Chain with Partial Integrability
• Density Matrix Renormalization Group Method for 2D Classical Models
• Ageing phenomena without detailed balance: the contact process
• Exact solution of a 1D asymmetric exclusion model using a matrix formulation
• Density matrix renormalization group study of the correlation function of the bilinear-biquadratic spin-1 chain
• Lanczos Algorithms for Large Symmetric Eigenvalue Computations
• Stable Optimization of a Tensor Product Variational State
• Emptiness Formation Probability for the One-Dimensional IsotropicXYModel
• Critical properties of S= 1/2 antiferromagnetic XXZ chain with next-nearest-neighbour interactions
• A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
• The density matrix renormalization group applied to single-particle quantum mechanics
• Time-Dependent Statistics of the Ising Model
• Single-block renormalization group: quantum mechanical problems

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