New Trends in Density Matrix Renormalization

TL;DR

This paper reviews recent advances and diverse applications of the Density Matrix Renormalization Group (DMRG), highlighting its extensions to dynamical properties, finite temperature, quantum information, and ab initio molecular calculations.

Contribution

It provides a comprehensive overview of the latest developments and broadening scope of DMRG beyond condensed matter physics.

Findings

DMRG now applied in quantum chemistry and high energy physics

Development of time-dependent and finite temperature algorithms

DMRG as an impurity solver in dynamical mean field theory

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.