Unifying Projected Entangled Pair States contractions

The approximate contraction of a Projected Entangled Pair States (PEPS) tensor network is a fundamental ingredient of any PEPS algorithm, required for the optimization of the tensors in ground state search or time evolution, as well as for the evaluation of expectation values. An exact contraction is in general impossible, and the choice of the approximating procedure determines the efficiency and accuracy of the algorithm. We analyze different previous proposals for this approximation, and show that they can be understood via the form of their environment, i.e. the operator that results from contracting part of the network. This provides physical insight into the limitation of various approaches, and allows us to introduce a new strategy, based on the idea of clusters, that unifies previous methods. The resulting contraction algorithm interpolates naturally between the cheapest and most imprecise and the most costly and most precise method. We benchmark the different algorithms with finite PEPS, and show how the cluster strategy can be used for both the tensor optimization and the calculation of expectation values. Additionally, we discuss its applicability to the parallelization of PEPS and to infinite systems (iPEPS).Comment: 28 pages, 15 figures, accepted versio

Mechatronic Design: A Port-Based Approach

In this paper we consider the integrated design of a mechatronic system. After considering the different design steps it is shown that a port-based approach during all phases of the design supports a true mechatronic design philosophy. Port-based design enables use of consistent models of the system throughout the design process, multiple views in different domains and reusability of plant models, controller components and software processes. The ideas are illustrated with the conceptual and detailed design of a mobile robot

Monte Carlo simulation with Tensor Network States

It is demonstrated that Monte Carlo sampling can be used to efficiently extract the expectation value of projected entangled pair states with large virtual bond dimension. We use the simple update rule introduced by Xiang et al. to obtain the tensors describing the ground state wavefunction of the antiferromagnetic Heisenberg model and evaluate the finite size energy and staggered magnetization for square lattices with periodic boundary conditions of sizes up to L=16 and virtual bond dimensions up to D=16. The finite size magnetization errors are 0.003(2) and 0.013(2) at D=16 for a system of size L=8,16 respectively. Finite D extrapolation provides exact finite size magnetization for L=8, and reduces the magnetization error to 0.005(3) for L=16, significantly improving the previous state of the art results.Comment: 6 pages, 7 figure