Density Matrix Renormalization Group

The density-matrix renormalization  group (DMRG) is the most powerful  numerical method for simulating one-dimenional quantum lattice models.

1975 Kenneth K. Wilson solved the single-impurity Kondo model using the numerical renormalization group

1992 Steven R White published the first paper on the DMRG.

Some extensions of the DMRG we  proposed:

• Momentum space DMRG: This is the approach for performing DMRG calculations in momentum space, or more generally in  other basis space with non-local and off-diagonal interactions, such as the angular momentum space and the Hartree-Fock basis space used in the Quantum Chemistry calculations

• Quantum transfer-matrix renormalization group [Refs 1 & 2]: this is the most accurate numerical method for evaluating thermodynamic quantities of 1D quantum lattice models. 

• Pace-keeping DMRG: this is the method for solving a time-dependent Schrodinger equation of many interacting particles.