Density Matrix Renormalization Group on distributed GPUs*

The density matrix renormalization group (DMRG) algorithm is the most successful numerical method for simulating the statics and dynamics of one-dimensional quantum lattice systems. Applications of DMRG in higher dimensions are exceedingly expensive because of the need for large bond dimensions. In this work, we demonstrate the use of graphical processing units (GPU), which can massively parallelize the numerical linear algebra calculations, for accelerating DMRG simulation. Compared to the CPU, the memory bandwidth, computing power, and interconnect speed of GPU clusters are significantly improved, which makes it a promising solution for performing large-scale DMRG calculations. Besides, we apply architecture-aware optimizations, such as mixed precision linear algebra and kernel fusion, to further improve the performance of DMRG on distributed GPUs.