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Bulletin of the American Physical Society

Applications of projected entangled-pair states to two-dimensional spin systems

Bela Bauer, Guifré Vidal, Matthias Troyer

Published Mar 15, 2010• 0 citations
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We have applied a variational algorithm based on projected entangled pair states (PEPS) to a two dimensional frustrated spin system, the spin-1/2 antiferromagnetic Heisenberg model on the Shastry-Sutherland lattice. We use the class of PEPS with internal tensor dimension D=2 , the first step beyond product states (D=1 PEPS). We have found that the D=2 variational PEPS algorithm is able to capture the physics in both the valence-bond crystal and the Néel ordered state. Also the spin textures giving rise to the magnetization plateaus seen in experiments on SrCu2(BO3)(2) are well reproduced. This shows that PEPS with the smallest nontrivial internal dimension, D=2 , can provide valuable insights into frustrated spin systems.
In the numerical calculation, the projected entangled pair state (PEPS) algorithm is the most important tensor network algorithm for two-dimensional strongly correlated electron quantum lattice system. In this paper, the optimization of PEPS for two-dimensional quantum system is discussed. An optimization connection between how to update the PEPS tensor and how to calculate the physical observable is investigated, for the tensor network algorithm based on the PEPS representation, which can greatly improve the utilization of computing resources. In this case, optimized PEPS algorithm, as a powerful tool, can be used to study quantum phase transitions and quantum critical phenomena in the thermodynamic limit of the two-dimensional strongly correlated electron quantum lattice system. Of course, optimization of PEPS algorithm program has many other applications, such as adding U(1) and SO(2) symmetry in PEPS algorithm, etc.