Title: Efficient calculation of three-dimensional tensor networks

Speaker: Liping Yang， Chongqing University

Time: 10:00 am, 2023-7-18 Tuesday

Location: Room C302, Science Building, Tsinghua University

Abstract:

We have proposed an efficient algorithm to calculate physical quantities in the translational invariant three-dimensional tensor networks, which is particularly relevant to the study of the three-dimensional classical statistical models and the (2+1)-dimensional quantum lattice models. In the context of a classical model, we determine the partition function by solving the dominant eigenvalue problem of the transfer matrix, whose left and right dominant eigenvectors are represented by two projected entangled simplex states. These two projected entangled simplex states are not Hermitian conjugate to each other but are appropriately arranged so that their inner product can be computed much more efficiently than in the usual prescription. For the three-dimensional Ising model, the calculated internal energy and spontaneous magnetization agree with the published results in the literature. The possible improvement and extension to other models are also discussed.

Refs: Phys. Rev. B 107, 165127 (2023)

Brief CV: Associate Professor Li-Ping Yang acquired her Ph.D in the institute of theoretical physics, Chinese academy of Sciences in 2009. Then she subsequently worked in Materials Science, Japan, Leiden University, Netherlands, IFW-dresden, Germany, and Beijing Computational Science Research Center. In 2012, she joined in Chongqing university. Her research interests include : phase and phase transition, and the development and employment of tensor network algorithms.