New Trends in Density Matrix Renormalization
arXiv:cond-mat/0609039 · doi:10.1080/00018730600766432
Abstract
The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and thermodynamic properties. Its field of applicability has now extended beyond Condensed Matter, and it is now successfully used in Quantum Chemistry, Statistical Mechanics, Quantum Information Theory, Nuclear and High Energy Physics as well. In this article, we briefly review the main aspects of the method and present some of the most relevant applications so as to give an overview on the scope and possibilities of DMRG. We focus on the most important extensions of the method such as the calculation of dynamical properties, the application to classical systems, finite temperature simulations, phonons and disorder, field theory, time-dependent properties and the ab initio calculation of electronic states in molecules. The recent quantum information interpretation, the development of highly accurate time-dependent algorithms and the possibility of using the DMRG as the impurity-solver of the Dynamical Mean Field Method (DMFT) give new insights into its present and potential uses. We review the numerous very recent applications of these techniques where the DMRG has shown to be one of the most reliable and versatile methods in modern computational physics.
Review article (54 pages)
References in corpus (34)
- Real time evolution using the density matrix renormalization group
- Matrix Product Density Operators: Simulation of finite-T and dissipative systems
- Matrix product states represent ground states faithfully
- DMRG and periodic boundary conditions: a quantum information perspective
- Entanglement versus Correlations in Spin Systems
- Diverging Entanglement Length in Gapped Quantum Spin Systems
- Time-step targetting methods for real-time dynamics using DMRG
- Spin-charge separation in cold Fermi-gases: a real time analysis
- Phase diagram of spin-1 bosons on one-dimensional lattices
- Dimerization in a half-filled one-dimensional extended Hubbard model
- Phase Diagram of a Spin Ladder with Cyclic Four Spin Exchange
- Tomonaga-Luttinger parameters for doped Mott insulators
- Time evolution of one-dimensional Quantum Many Body Systems
- Frustrated three-leg spin tubes: from spin 1/2 with chirality to spin 3/2
- Broken time-reversal symmetry in strongly correlated ladder structures
- Comment on "Time-Dependent Density-Matrix Renormalization Group: A Systematic Method for the Study of Quantum Many-Body Out-of- Equilibrium Systems"
- Real-time dynamics at finite temperature by DMRG: A path-integral approach
- Dimerization induced by the RKKY interaction
- Density-matrix renormalisation group approach to quantum impurity problems
- Renormalization-group analysis of the one-dimensional extended Hubbard model with a single impurity
- High Energy Dynamics of the Single Impurity Anderson Model
- Investigation of Quantum Phase Transitions using Multi-target DMRG Methods
- Spectral Densities from Dynamic Density-Matrix Renormalization
- Thermodynamics and Crossover Phenomena in the Correlation Lengths of the One-Dimensional t-J Model
- Density matrix renormalization group and wave function factorization for nuclei
- Response to ``Comment on `time-dependent density-matrix renormalization group: a systematic method for the study of quantum many-body out-of-equilibrium systems''' by H. G. Luo, T. Xiang, and X. Q. Wang
- Small Fermi surface in the one-dimensional Kondo lattice model
- Ferromagnetic polarons in the one-dimensional ferromagnetic Kondo model with quantum mechanical S=3/2 core spins
- Quantum anisotropic Heisenberg chains with superlattice structure: a DMRG study
- Disorder-induced phases in the S=1 antiferromagnetic Heisenberg chain
- Doped two-leg ladder with ring exchange
- Ground-state phases in antiferromagnetic spin-crossover chains
- Real-space renormalization group approach for the corner Hamiltonian
- Correlation effects for semiconducting single wall carbon nanotube: a density matrix renormalization group study
Cited by in corpus (14)
- The numerical renormalization group method for quantum impurity systems
- Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
- Scaling of entanglement support for Matrix Product States
- Vector chiral and multipolar orders in the spin-1/2 frustrated ferromagnetic chain in magnetic field
- Transport properties and Kondo correlations in nanostructures: the time-dependent DMRG method applied to quantum dots coupled to Wilson chains
- Simulation of time evolution with the MERA
- Density matrix renormalization group approach to two-fluid open many-fermion systems
- Incommmensurability and unconventional superconductor to insulator transition in the Hubbard model with bond-charge interaction
- Correlation Effects on Atom Density Profiles of 1-D and 2-D Polarized Atomic-Fermi-Gas Loaded on Optical Lattice
- Stripe Formation in Fermionic Atoms on 2-D Optical Lattice inside a Box Trap: DMRG Studies for Repulsive Hubbard Model with Open Boundary Condition
- Mott Phase in Polarized Two-component Atomic Fermi Lattice Gas:A Playground for S=1/2 Heisenberg Model in Magnetic Field
- Hole Localization in One-Dimensional Doped Anderson-Hubbard Model
- Dimerization process and elementary excitations in spin-Peierls chains coupled by frustrated interactions
- An Improved Initialization Procedure for the Density-Matrix Renormalization Group