Density Matrix Renormalization Group - Technical Details About The Implementation

Technical Details About The Implementation

A practical implementation of the DMRG algorithm is a lengthy work. A few of the main computational tricks are these:

• The ground state for the superblock is obtained using the Lanczos algorithm of matrix diagonalization. Another choice is the Arnoldi method, especially when dealing with non-hermitian matrices.

• The Lanczos algorithm usually starts with a random seed. In DMRG, the ground state obtained in a certain DMRG step, suitably transformed, may serve as a better seed for the Lanczos algorithm at the next DMRG step.

• In systems with symmetries, we may have conserved quantum numbers, such as total spin in a Heisenberg model (quantum). It is convenient to find the ground state within each of the sectors into which the Hilbert space is divided.

• An example: dmrg of Heisenberg model