Momentum Space DMRG and Quantum Chemistry Calculations


The first work on the momentum space DMRG was published in 1996:

T. Xiang, Density-matrix renormalization-group method in momentum space, Physical Review B 53, R10445 (1996)

This paper removes the barrier in the extension of the DMRG from the real space to the momentum space, or more generally to any other basis space, at which the interaction is non-local and off-diagonal.  It sets the foundation for carrying the DMRG calculation not only in the momentum space, but also in the  Quantum Chemistry study. 

In the real space, the interaction is generally local and diagonal, and the effort in evaluating and storing these interaction terms scales linearly with the lattice size N. However, in the momentum space (or in the quantum chemistry calculation), the interaction contains at least N3  terms. This obstructs the application of the DMRG if all these terms have to be handled independently.