Exploiting the Hermitian symmetry in tensor network algorithms

Abstract

Exploiting symmetries in tensor network algorithms plays a key role for reducing the computational and memory costs. Here we explain how to incorporate the Hermitian symmetry in double-layer tensor networks, which naturally arise in methods based on projected entangled-pair states (PEPS). For real-valued tensors the Hermitian symmetry defines a ${\mathbb{Z}}_2$ symmetry on the combined bra and ket auxiliary level of the tensors. By implementing this symmetry, a speedup of the computation time by up to a factor 4 can be achieved, while expectation values of observables and reduced density matrices remain Hermitian by construction. Benchmark results based on the corner transfer matrix renormalization group (CTMRG) and higher-order tensor renormalization group (HOTRG) are presented. We also discuss how to implement the Hermitian symmetry in the complex case, where a similar speedup can be achieved.

7 pages, 4 figures

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Cited by in corpus (3)

• Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach
• Single-layer framework of variational tensor network states
• Accelerating two-dimensional tensor network contractions using QR decompositions