A major advance in density-matrix renormalization group (DMRG) calculations has been achieved by the invention of highly efficient DMRG techniques for the simulation of real-time dynamics of strongly correlated quantum systems in one dimension. Starting from established linear-response techniques in DMRG and early attempts at real-time dynamics, we go on to review two current methods which both implement the idea of adapting the effective Hilbert space of DMRG to the quantum state evolving in time. We also give an outlook on extensions to finite temperature calculations.
A major advance in density-matrix renormalization group (DMRG) calculations has been achieved by the invention of highly efficient DMRG techniques for the simulation of real-time dynamics of strongly correlated quantum systems in one dimension. Starting from established linear-response techniques in DMRG and early attempts at real-time dynamics, we go on to review two current methods which both implement the idea of adapting the effective Hilbert space of DMRG to the quantum state evolving in time. We also give an outlook on extensions to finite temperature calculations.
A major advance in density‐matrix renormalization group (DMRG) calculations has been achieved by the invention of highly efficient DMRG techniques for the simulation of real‐time dynamics of strongly correlated quantum systems in one dimension. Starting from established linear‐response techniques in DMRG and early attempts at real‐time dynamics, we go on to review two current methods which both implement the idea of adapting the effective Hilbert space of DMRG to the quantum state evolving in time. We also give an outlook on extensions to finite temperature calculations.
In this paper recent substantial progress in applying the density-matrix renormalization-group (DMRG) to the simulation of the time-evolution of strongly correlated quantum systems in one dimension is reviewed. Various approaches to generating a time-evolution numerically are considered. The key focus of this review is on current strategies to circumvent the limitations of the quite small subspace well approximated by DMRG, by either enlarging or changing it as time evolves. All these approaches can be extended to the simulation of mixed, i.e. finite-temperature states. While this paper is phrased almost entirely in standard DMRG language, I finish by considering the alternative formulation of time-evolutions in the language of matrix product states which is less well-known but conceptually more powerful.
(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.
Ulrich Schollwo¨ck Arnold Sommerfeld Center for Theoretical Physics, University of Munich, Germany Since its invention in 1992 by White [1,2], the density matrix renormalization group (DMRG) has firmly established itself as the currently most powerful method to calculate static and more recently also dynamic [3-5] properties of low-lying eigenstates of strongly correlated Hamiltonians defined on onedimensional quantum lattices. At the same time, its extension to the analysis of two-dimensional classical [6] and one-dimensional quantum [7,8] transfer matrices has given access to highly precise thermodynamics in classical two-dimensional and quantum one-dimensional systems. It has even been extended to the numerically much more demanding study of non-Hermitian (pseudo-)Hamiltonians emerging in the analysis of classical steady states in one-dimensional systems [9-11]. However, it also turned out quite quickly that extending DMRG to the study of two-dimensional systems did not lead to similarly huge successes.
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.