GPU accelerated tensor contractions in the plaquette renormalization scheme

J. F. Yu, H. C. Hsiao, Ying-Jer Kao
Department of Physics and Center for Quantum Science and Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei, Taiwan 106
Computers & Fluids (04 November 2010)


   title={GPU accelerated tensor contractions in the plaquette renormalization scheme},

   author={Yu, JF and Hsiao, H.C. and Kao, Y.J.},

   journal={Computers & Fluids},





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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.
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