Efficient calculation of three-dimensional tensor networks

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.

8 pages, 10 figures

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Cited by in corpus (8)

• Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications
• Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices
• Tensor network Monte Carlo simulations for the two-dimensional random-bond Ising model
• The Green's function Monte Carlo combined with projected entangled pair state approach to the frustrated $J_1$-$J_2$ Heisenberg model
• Single-layer tensor network approach for three-dimensional quantum systems
• Efficient optimization of variational tensor-network approach to three-dimensional statistical systems
• A hybrid method integrating Green's function Monte Carlo and projected entangled pair states
• Single-layer framework of variational tensor network states