GPU accelerated tensor contractions in the plaquette renormalization scheme

We use the graphical processing unit (GPU) to accelerate the tensor contractions, which is the most time consuming operations in the variational method based on the plaquette renormalized states. Using a frustrated Heisenberg J₁–J₂ model on a square lattice as an example, we implement the algorithm based on the compute unified device architecture (CUDA). For a single plaquette contraction with the bond dimensions C = 3 of each rank of the tensor, results are obtained 25 times faster on GPU than on a current CPU core. This makes it possible to simulate systems with the size 8 × 8 and larger, which are extremely time consuming on a single CPU. This technology successfully relieves the computing time dependence with C, while in the CPU serial computation, the total required time scales both with C and the system size.