Error Analysis of the Density-Matrix Renormalization Group Algorithm for a Chain of Harmonic Oscillators

We investigate the application of the density-matrix renormalization group (DMRG) algorithm to a one-dimensional harmonic oscillator chain and compare the results with exact solutions, aiming at improving the algorithm's efficiency. It is demonstrated that the algorithm can show quite accurate results if the procedure is properly organized; for example, by using the optimized bases. The errors of calculated ground state energy and the energy gap between the ground state and the first excited state are analyzed, and they are found to be critically dependent upon the size of the system or the energy level structure of the studied system and the number of states targeted during the DMRG procedure.