Two-dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method

We present a hybrid numerical approach to simulate quantum many-body problems on two spatial dimensional quantum lattice models via the non-Abelian ab initio version of the density matrix renormalization group method on state-of-the-art high-performance computing infrastructures. We demonstrate that for the two-dimensional spinless fermion model and for the Hubbard model on torus geometry, altogether several orders of magnitude in computational time can be saved by performing calculations on an optimized basis and by utilizing hybrid CPU-multiGPU parallelization. At least an order of magnitude reduction in computational complexity results from mode optimization, while a further order of reduction in wall time is achieved by massive parallelization. Our results are measured directly in the number of floating point operations and seconds. A detailed scaling analysis of the obtained performance as a function of matrix ranks and as a function of system size up to 12 x 12 lattice topology is discussed. Our CPU-multiGPU model also tremendously accelerates the calculation of the one- and two-particle reduced density matrices, which can be used to construct various order parameters and trace quantum phase transitions with high fidelity.