PEPS++: Towards Extreme-Scale Simulations of Strongly Correlated Quantum Many-Particle Models on Sunway TaihuLight

Abstract

The study of strongly frustrated magnetic systems has drawn great attentions from both theoretical and experimental physics. Efficient simulations of these models are essential for understanding their exotic properties. Here we present PEPS++, a novel computational paradigm for simulating frustrated magnetic systems and other strongly correlated quantum many-body systems. PEPS++ can accurately solve these models at the extreme scale with low cost and high scalability on modern heterogeneous supercomputers. We implement PEPS++ on Sunway TaihuLight based on a carefully designed tensor computation library for manipulating high-rank tensors and optimize it by invoking various high-performance matrix and tensor operations. By solving a 2D strongly frustrated J 1 -J 2 model with over ten million cores, PEPS++ demonstrates the capability of simulating strongly correlated quantum many-body problems at unprecedented scales with accuracy and timeto-solution far beyond the previous state of the art.

Stable diagonal stripes in the t–J model at n̅h = 1/8 doping from fPEPS calculations

“…More details of the methods are discussed in refs. [34][35][36] . It is well known that the environment effects are oversimplified in the SU method.…”

“…The projected entangled pair states method (PEPS) [24][25][26][27][28][29] , and its generalization to fermionic systems (fPEPS) [30][31][32][33] provide systematically improvable variational wave functions for many-body problems. In recent works, we developed a gradient method combined with Monte Carlo sampling techniques to optimize the (f)PEPS wave functions with controlled accuracy [34][35][36] . This method significantly reduces the scaling with respect to the bond dimension D, thereby allowing a much larger bond dimension to be used, resulting in highly accurate and converged results for large finite systems.…”

Simulation of the Ring-exchange Models with Projected Entangled Pair States

“…Because of the drastic approximation to the environment (even for the cluster environment) during the ITE, the resulting ground state may not be accurate enough. It has been demonstrated that the gradient optimization after ITE can significantly improve the ground state energies for the bond interaction models, where the energy and the gradients are calculated via a Monte Carlo sampling technique with relative low time complexity [44,54,55]. These techniques can also be applied to the ring-exchange models in a similar manner.…”

Loop-free tensor networks for high-energy physics

“…By quantitatively validating quantum simulators in out-of-equilibrium situations, even if only in lower dimensions, MPS and TN methods play a very important role towards establishing quantum simulators as reliable tools in quantum physics. Finally, recently the applications of TN to higher-dimensional LGTs has start becoming within reach of the available algorithms and numerical resources [51][52][53][54][55][56][57], providing an important stimulus to further develop these techniques and explore their application to LGTs.…”