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Information × Registration Number 0224U001174, 0122U001575 , R & D reports Title Magnetic properties of mesoscopic systems with internal degrees of freedom popup.stage_title Head Ratkevych Serhii S., Кандидат фізико-математичних наук Registration Date 18-01-2024 Organization V.N. Karazin Kharkiv National University popup.description2  The goal of the research is to build modern numerical algorithms that favorably describe the multiparticle states and magnetic properties of mesoscopic systems with sufficient accuracy, as well as provide an opportunity to transmit a number of new physical effects. A method of variational optimization of infinite projected states of an entangled pair on a cellular lattice has been developed. The method is based on the automatic differentiation of groups of renormalization of the angular transition matrix. The approach is applied to Heisenberg antiferromagnetic model with spin -1/2 and Kitaev ferromagnetic model on a honeycomb lattice. The developed formalism gives several accurate results for the main physical observables and has the necessary potential for further extension. This study aims to establish that other effective reduction methods on other grids can lead to a stable variational update with gradients obtained by automatic differentiation. This research focuses on the generalization of the angular matrix renormalization group approach transferred to the cellular lattice tensor network. This study opens several directions for future research. The algorithm can be naturally applied to frustrated Heisenberg antiferromagnets with long-range interactions. With certain technical modifications, it can also be used for a triangular geometric lattice. In addition, it would be interesting to generalize the method to larger unit cells. Application of the variational method of infinite projection entangled pair states to hyperbolic lattice geometry, something that has long been implemented in experiments, is another possible direction of research. Finally, automatic differentiation can be effectively applied to the tensor group method of renormalization and its modifications. This paves the way for variational optimization of the method of infinite projection entangled pair states with tensor renormalization. Product Description popup.authors Bulakhov Mykyta S. Lazuryk Valentyna Mykhaylivna Lukin Illia V. Naumovets Artem S. Peletminskii Oleksander S Petrenko Oleksiy L. Rudychev Yegor . V. Sotnikov Andrii G. popup.nrat_date 2024-01-18 Close