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double-layer tensor network

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22 - Two-Dimensional Tensor Network States
Tao Xiang, Chinese Academy of Sciences, Beijing
Book:

Density Matrix and Tensor Network Renormalization

Published online:

18 January 2024

Print publication:

31 August 2023, pp 351-363
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Summary

This chapter discusses the methods of solving PEPS or other two-dimensional tensor network states, including variational optimization and the annealing simulation. The variation optimization determines the local terms by minimizing the ground-state energy. The annealing simulation takes the full or simple update strategy to filter out the ground state through the imaginary time evolution. The nonlinear effect arises in evaluating the derivative of uniform PEPS and is avoided by utilizing automatic differentiation. Both variational optimization and the annealing simulation involve a contraction of double-layer tensor network states. This contraction is the primary technical barrier in the study of PEPS. A nested tensor network approach is introduced to combat this difficulty.