New trends in density matrix renormalization

By Karen Hallberg. 2006

270 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Physical and Theoretical Chemistry

View Paper: https://www.semanticscholar.org/paper/80105c8fc90fdc787195fb0dfaf8fe715a572590

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

In Physical and Theoretical Chemistry

Citations in the corpus

The mass spectrum of the Schwinger model with matrix product states (2013, background): “In DMRG it is possible to target several of the lowest eigenstates [41], or, in the case of a first excited state with a distinct quantum number, to run the ground state search in different sectors.”
Continuous-time Monte Carlo methods for quantum impurity models (2010, methodology): “The “numerical renormalization group” (NRG) methods are based on iterative diagonalization using a logarithmic discretization of the energy spectrum of the lead states and are reviewed for example in (Bulla et al., 2008) while the “density matrix renormalization group” (DMRG) techniques involve an i”
Spreading of correlations and entanglement after a quench in the one-dimensional Bose–Hubbard model (2008, methodology): “We show in figure 1 the von Neumann entropy of the static Bose–Hubbard model with open boundary conditions for different interaction strengths U/J obtained using DMRG calculations on a system of length L = 1024.”
Numerical renormalization group method for quantum impurity systems (2007, methodology): “Let us conclude this section with a few remarks on the relation between the NRG and the density matrix renormalization group method (DMRG), which is widely used for the investigation of one-dimensional interacting systems (Hallberg, 2006; Noack and Manmana, 2005; Schollwöck, 2005).”
Matrix product states and projected entangled pair states: Concepts, symmetries, theorems (2020, background): “While there are many reviews on that topic (Biamonte, 2019; Bridgeman and Chubb, 2017; Cirac and Verstraete, 2009; Hallberg, 2006; Orus, 2014; Schollwöck, 2005, 2011; Verstraete et al., 2008) the vast majority focus on the practical aspects of tensor networks; in particular, on how to use them in…”
Engineered Open Systems and Quantum Simulations with Atoms and Ions (2012, background): “…1995; Prokof’ev et al., 1998), coupled-cluster expansion (Shavitt and Bartlett, 2009; Hammond et al., 1994), density functional theory (Parr and Yang, 1989), dynamical mean field theories (Georges et al., 1996), and density matrix renormalization group (DMRG) (Schollwöck, 2005; Hallberg, 2006).”