Abstract. The Density Matrix Renormalization Group (DMRG) was introduced by Steven White in 1992 as a method for accurately describing the properties of onedimensional quantum lattices. The method, as originally introduced, was based on the iterative inclusion of sites on a real-space lattice. Based on its enormous success in that domain, it was subsequently proposed that the DMRG could be modified for use on finite Fermi systems, through the replacement of real-space lattice sites by an appropriately ordered set of single-particle levels. Since then, there has been an enormous amount of work on the subject, ranging from efforts to clarify the optimal means of implementing the algorithm to extensive applications in a variety of fields. In this article, we review these recent developments. Following a description of the realspace DMRG method, we discuss the key steps that were undertaken to modify it for use on finite Fermi systems and then describe its applications to Quantum Chemistry, ultrasmall superconducting grains, finite nuclei and two-dimensional electron systems. We also describe a recent development which permits symmetries to be taken into account consistently throughout the DMRG algorithm. We close with an outlook for future applications of the method.
Abstract. The Density Matrix Renormalization Group (DMRG) was introduced by Steven White in 1992 as a method for accurately describing the properties of onedimensional quantum lattices. The method, as originally introduced, was based on the iterative inclusion of sites on a real-space lattice. Based on its enormous success in that domain, it was subsequently proposed that the DMRG could be modified for use on finite Fermi systems, through the replacement of real-space lattice sites by an appropriately ordered set of single-particle levels. Since then, there has been an enormous amount of work on the subject, ranging from efforts to clarify the optimal means of implementing the algorithm to extensive applications in a variety of fields. In this article, we review these recent developments. Following a description of the realspace DMRG method, we discuss the key steps that were undertaken to modify it for use on finite Fermi systems and then describe its applications to Quantum Chemistry, ultrasmall superconducting grains, finite nuclei and two-dimensional electron systems. We also describe a recent development which permits symmetries to be taken into account consistently throughout the DMRG algorithm. We close with an outlook for future applications of the method.
The density matrix renormalization group (DMRG) was introduced by Steven White in 1992 as a method for accurately describing the properties of one-dimensional quantum lattices. The method, as originally introduced, was based on the iterative inclusion of sites on a real-space lattice. Based on its enormous success in that domain, it was subsequently proposed that the DMRG could be modified for use on finite Fermi systems, through the replacement of real-space lattice sites by an appropriately ordered set of single-particle levels. Since then, there has been an enormous amount of work on the subject, ranging from efforts to clarify the optimal means of implementing the algorithm to extensive applications in a variety of fields. In this article, we review these recent developments. Following a description of the real-space DMRG method, we discuss the key steps that were undertaken to modify it for use on finite Fermi systems and then describe its applications to quantum chemistry, ultrasmall superconducting grains, finite nuclei and two-dimensional electron systems. We also describe a recent development which permits symmetries to be taken into account consistently throughout the DMRG algorithm. We close with a description of the outlook for future applications of the method.
(April 2006) 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 is 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
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 is successfully used in quantum chemistry, statistical mechanics, quantum information theory, and 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 of 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.
A new approach to large-scale nuclear structure calculations, based on the density matrix renormalization group (DMRG), is described. The DMRG method, which was developed originally in the framework of low-dimensional quantum lattices, has recently been extended to finite Fermi systems. Following a general description of this extended DMRG methodology, we briefly review its first application to a pairing hamiltonian. We then discuss its application to a schematic nuclear model involving many identical nucleons constrained to move in a single large-j shell. In those cases in which exact diagonalization of the hamiltonian is possible, the method is able to reproduce the exact results with extreme precision. Results are also presented for a model problem in which exact solution is not feasible.
The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to nanoscopic and 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 is 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. 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 whe the DMRG has shown to be one of the most reliable and versatile methods in modern computational physics.
The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This algorithm has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly become the method of choice for numerical studies of such systems. Its applications to the calculation of static, dynamic, and thermodynamic quantities in these systems are reviewed here. The potential of DMRG applications in the fields of two-dimensional quantum systems, quantum chemistry, three-dimensional small grains, nuclear physics, equilibrium and nonequilibrium statistical physics, and time-dependent phenomena is also discussed. This review additionally considers the theoretical foundations of the method, examining its relationship to matrix-product states and the quantum information content of the density matrices generated by the DMRG.