Large-Scale Implementation of the Density Matrix Renormalization Group Algorithm

The density matrix renormalization group (DRMG) algorithm, a numerical technique that has been successfully used for investigating the low energy properties of one-dimensional (1D) strongly correlated quantum systems, has recently emerged as an effective tool for studying two-dimensional (2D) systems as well. At the core of DMRG is a general decimation procedure that allows the systematic truncation of the Hilbert space leaving only the most relevant basis states. However, studying 2D systems requires more degrees of freedom and greater computational resources. To address this computational roadblock, we develop a massively parallel implementation of the DMRG algorithm that targets a large number of basis states. It relies on parallel linear algebra libraries that distribute the generation and diagonalization of large sparse matrices, as these remain to be the most time-consuming steps in DMRG. We tailor our developed code for efficient performance on two sections of CINECA Marconi, a class Tier-0 supercomputing infrastructure, and evaluate its performance and scalability on up to thousands of processors. From the performance analysis we identify some limitations in scalability and suggest possible ways to rectify them.