The density-matrix renormalization group

By Ulrich Schollwoeck. 2004

1,291 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/b1b7400f06f64f3dd05e4349896ec11dcd578454

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

The nonperturbative functional renormalization group and its applications (2020, methodology): “3The RG has also been used as a mathematical tool for a rigorous non-perturbative construction of field theories [16–20], and as a nonperturbative computational tool, such as Wilson’s numerical RG for the Kondo problem [21] or the density matrix renormalization group (DMRG) for one-dimensional latti”
Quantum spin liquid states (2016, methodology): “The DMRG method (White, 1992) and its generalizations (Schollwöck, 2005) can be viewed as systematic approaches for constructing MPS variational wavefunctions as the size of the system gradually increases.”
Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions (2013, neutral): “, [53].”
Adiabatic Quantum Computing (2016, background): “…time whether universal AQC is possible in 1D, with some suggestive evidence to the contrary, such as the impressive success of density matrix renormalization group (DMRG) techniques in calculating ground state energies and other properties of a variety of 1D quantum systems (Schollwöck, 2005).”
Entanglement entropy and conformal field theory (2009, methodology): “t;0 (and not only for n≥ 1) at least for the simplest solvable models, where it can be explicitly checked. This is of relevance for the convergence of of the algorithms based on matrix product states [27, 28]. 3.1. Generalizations: Finite temperature or ﬁnite size The fact that Trρn A transforms und”
Continuous-time Monte Carlo methods for quantum impurity models (2010, methodology): “Starting from work of Wilson (1975) and subsequently of White (1992), (see (Schollwöck, 2005) for a review), an important set of numerical methods has been developed based on intelligently chosen truncations of the 5 Hilbert space of the many-body problem in question.”
Electronic structure calculations with dynamical mean-field theory (2005, neutral): “Phys., Vol. 78, No. 3, July–September 2006 Dagotto, 1994 , density-matrix renormalization-group methods White, 1992; Schollwöck, 2005 , and so on.”