The density-matrix renormalization group

Details The density-matrix renormalization group The density-matrix renormalization group

2004-09-11

arxiv.org/abs/cond-mat/0409292v1

Rev. Mod. Phys. 77, 259 (2005)

Physics

Condensed Matter

Strongly Correlated Electrons

accepted by Rev. Mod. Phys. in July 2004; scheduled to appear in the January 2005 issue

Scientific paper

10.1103/RevModPhys.77.259

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 acquired the status of method of choice for numerical studies of one-dimensional quantum systems. Its applications to the calculation of static, dynamic and thermodynamic quantities in such systems are reviewed. The potential of DMRG applications in the fields of two-dimensional quantum systems, quantum chemistry, three-dimensional small grains, nuclear physics, equilibrium and non-equilibrium statistical physics, and time-dependent phenomena is discussed. This review also 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 DMRG.

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